I am teaching my Yellow Shoulder Amazon, Salty, to do this trick too. It's a very hard trick to learn! The way I am doing it, is first I taught Salty to STAY, or station himself on the pedals, with his feet only on the pedals - that took a while for him to learn. We use the "Stay" command in another trick, so he understands that part of it. Once he realized his feet can only be on the pedals, i started to lead him with a treat in one hand and helping the bike to move forward with the other hand, in the back of the bike. Thats where we are now or maybe a little more than that. He remains planted on the bike with his feet on the pedals for about 2 revolutions of the pedals (which is about all the room I have for the trick) and occasionally I will remove my hand from the back of the bike and he propels the bike with his feet. As I said, this is a really hard trick for them to learn. We dont practice this one every night, maybe once or twice a week, because I rotate the tricks every night so Salty doesn't get bored. I would get the "Stay" part down really well before moving on.
Some general tips for trick training:
Be consistent - always ask for the trick or action the same way every time, so you don't confuse the parrot. I use both verbal and hand signals with Salty for most tricks.
Be immediate - have the treat ready in one hand, so you can reward immediately when there is any progress, no matter how small.. Immediate, so the parrot can associate the action with the reward
Be patient! Parrots can be stubborn little mules sometimes. I took me a whole year+ of training every night with Salty to get him to the point where he putts his harness on without a big fuss. But, once they understand that training time is learning time, it becomes much easier. Not easier to do a given trick - that depends on the trick and the dexterity needed, but they will understand what you are asking them to do.
Other tips:
Try to begin and end each training session on a positive note, with tricks he loves to do and does well. That's a biggie, because you want training sessions to be something he looks forward to every day.
I set aside 15 minutes every day, at the same time, for training. We usually only do a given trick once in each session, or twice, if he really likes doing it. Training treats should be the parrots very favorite treat and used only in the training session. And it should be something he eats fairly quickly, so the session moves right along. Salty likes pine nuts and walnuts equally, but the takes his time eating walnuts, so we use pine nuts ( tiny pieces of them, maybe 1/3 or less of a pine nut) as his training treat.
Good luck! I think trick training is a great way to strengthen the bond and develop trust with your parrot.
AND lastly - where did you get the bicycle from? I like the design on yours a lot! Mine is made similar, but in aluminum and has a chain drive. The aluminum is heavy, the edges could be better rounded off and smoothed and the chain drive always makes me nervous he could get his foot or toe meshed into it.