NE - I did the London Triathlon last year; like you I swim badly, had no real cycling fitness and run a lot. I bought a bike, but kept on getting punctures... I ended up doing one 60min ride per week, and one 30min interval ride per week, both on an exercise bike. This worked pretty well - my bike leg was pretty good (and great fun). One thing I would recommend (I never did it) is to do some "bricks" - ie bike then run, or run then bike.