You have two things to focus:
1. A warm up that activates something called the lactic acid shuffle
2. A warm up that is specific to all muscles relevant to racing
In regards to the warm up, the exact muscles that you are going to be using to ride (especially fast) need to be activated and warm up prior to getting on the bike. I strongly suggest that you try a Concept 2 Rower. The rower literally hits every muscle in your body (verses just your legs on a spin bike). If you don't have access to a rower, then you need to add some upper body activity in addition to the spin bike.
Regarding the lactic acid shuffle: you need to throw is some short bursts of high intensity into your warm up to emmulate what happens when the gate drops. Notice that you are beginning to feel better (and you go faster) after a few laps have transpired. You want to make this happen PRIOR to the gate dropping - hence the quality and quantity of the warm up.
Please email directly at firstname.lastname@example.org
if you would like some pre-race warm up protocols.
If you don't notice a difference after a good/specific warm up, then you need to look into your intensity levels that you are training at (see Coach Seiji's notes- he is spot on).
Please keep up posted!