You don't keep the benefits for a super long time - it does depend somewhat on the conditions of the day - colder the day, the less time your warm up lasts. I've read you have 15 min or so of keeping your optimal warmed up condition. I'm guessing your bike probably has to be racked some hours before your race? Do you have a second bike you can warm up with? or perhaps you could warm up by running? Tri's don't really accommodate warming up for the bike much, as most people are warmed up from the swim, I guess.

(btw - that 1-1.5 hours usually includes some futzing around when it comes to bike racers.... getting your bike out of the trainer, changing wheels, changing clothes.... so you aren't really on the bike that whole time)