A similar principle applies to cycling. If I ride my motorbike to work, it's about 16 miles each way, which includes a 50mph stretch on the A40. JourneyPlanner did come up with quite a nice route for cycling, which involves parks and canal paths, but that's a bit longer: 19 miles each way, which they estimate at 2 hours. When I was 18, I could cycle for 15 miles without much trouble, but I'm not so sure about doing that now (particularly twice a day), and spending that long on travelling would take a big chunk out of my day. At the moment, my normal journey takes me 1h 15m each way (bus to station, two trains, bus to office), and I can read on the way so it's not entirely "dead time".
I could replace the bus journeys with cycling, but keep the train journeys: cycling would be a bit slower, but I wouldn't have to stand around at bus stops, so it should roughly balance out. However, you can't take full size bikes on trains during peak times. Also, I live in a first floor flat, so I don't really have space for a bike inside (plenty of clutter already!), and I've had two previous bikes stolen so I'm a bit wary of chaining one to a lamppost outside.
One potential solution is Oybike, which I first tried out in August 2006. The basic idea is that you have special docking stations spread around London, with yellow bikes chained to them. You sign up with their website, and give them some money for a pre-pay balance (like an Oyster card), then you can use this balance to pay for bike rental. For instance, there's a docking station at Willesden Junction, so I can pick up a bike from there: I have to phone in, give them the code on the screen, then they'll give me a code to unlock the bike. When I get to my destination, I connect the bike to another docking station and phone in again; they will then charge me a certain amount of money based on how long I had the bike for. It's optimised for short journeys, and in fact the first 30 minutes are now free.
It's a good idea, and I'd like to see it work, but it has a few flaws. Firstly, you need to have a docking station where you're going. That's not too bad where I work, but they're certainly not on every street corner. Similarly, the docking station needs to have an empty slot: if it's full of bikes already then you can't plug yours in. Either way, you'll then have to cycle around looking for somewhere to plug your bike in, then walk back to your actual destination. Secondly, you need to have a bike available at the start, otherwise you need to make alternate arrangements. That's not too bad if I can check the rack when I walk out of the station in the morning, but it's more of a problem when I leave in the evening, since the docking station at the hospital is in the opposite direction to the bus stop. Also, it affects journey planning: do I leave myself enough time to catch a bus in case there aren't any bikes? If so, I'll have to leave earlier and spend more time standing around on the cold station platform if there is a bike.
Another issue is human interaction. When I first used the system, you had to speak to someone on the phone to read out codes, so that meant that the bikes were only available during normal working hours (8am-6pm, I think). In my case, the bike would be more useful later in the evening, when the buses get less frequent. Since the whole system involves numeric codes, presumably it could be automated, and handled through text messages, so this may just have been a pilot system to iron out any kinks. I tried it again today, and the voicemail system suggested that you could type in numbers on your phone keypad (during a normal call), but I didn't have a chance to try this because the docking station was broken. I spoke to one of their operators, but he didn't seem particularly concerned about it; he just said that the batteries often drain in cold weather, so it should be fixed within a few days when their staff do routine checks.
As for the bikes themselves, they have baskets at the front, but these tend to get used as rubbish bins (since real bins are an Aid To Terrorists!), which is a nuisance. The rest of the fittings are a bit variable, e.g. the seat on the bike I looked at today had a big rip in it. When I hired one before, the bike slipped into freewheel mode when I tried changing gear, so the pedals whacked me in the back of the leg; I stayed in 3rd after that. If you want any protective gear (e.g. a helmet or a reflective jacket) then you need to provide that yourself, which is extra stuff to carry around with you, particularly if you then wind up taking the bus instead.
The map on their website has improved a lot recently (it used to be woefully out of date), but it reflects that they're confined to one part of London at the moment. In particular, there are no Oybikes in Croydon, so I wouldn't be able to use one at this end of my journey. All in all, I'd say that this is a reserve option (since I'm already registered) rather than something to rely on.
Another idea would be to get a folding bike, probably a Brompton. These are a lot more expensive than conventional bikes, but they do have advantages: you can carry them on trains and store them indoors (in a flat/office), since they don't take up much space when folded. My boss has one, and I'm impressed by the engineering involved. I wouldn't want to use one if I was at university (carrying it around to different lectures all day), but I could easily lift it in one hand, so I wouldn't have any trouble carrying it upstairs, and I wouldn't need to get the super lightweight titanium version. I tried it out by cycling up and down the corridor, and it works ok; it feels a bit different to a larger wheeled bike, and I'd need to get a telescopic seat pillar (since I'm a bit too tall for the standard one), but I think it would be fine for relatively short journeys. He's done 10 miles on it, but my bus journeys are only about 2 miles.
When I used to cycle in London, I had a lot of trouble with punctures (from broken glass on the roads), but kevlar tyres should solve that problem. I think the main limitation of the Brompton (and similar folding bikes) is that it's only really suited to roads, so it doesn't do very well on canal paths. When I lived in Sussex, I used to cycle to a summer job, and part of my journey was along the Downs link (connecting two ranges of hills), but that type of terrain is really more suited to a mountain bike. Still, how often am I really going to make that type of journey? I think it makes sense to optimise my normal route, then hire a different bike if I want to go on a cycling holiday in the countryside.
The interesting thing I've come across recently is the government's Green Transport Plan. Basically, you can get a bicycle tax-free if you mainly use it for commuting and it's bought through the company, and there are organisations like Cyclescheme who help out with the logistics. In my case, that would literally halve the cost: I could get a £600 bike for £301.27 (£25.11 for 12 months). The idea is that the company owns the bike, and they lease it to me. At the end of that time, they can choose to sell it to me at "fair market value"; doing a quick Google search, most companies seem to define this as 2.5% of the original purchase price, i.e. £15 for a £600 bike. Technically, the company can't promise to sell it to you, because it would then be a hire purchase scheme (and you'd lose the tax benefits), so there will presumably be an element of "nudge nudge, wink wink" going on. Anyway, our financial director is looking into that, and hopefully we can get that set up.
Action Bikes take part in Cyclescheme, and they also rent Brompton bikes (normally for 24 hours), so I think my best bet is to try one out and see how well it works on my normal commute, then take it from there.