The laws of physics will come into play here.
You can't generate more energy than you use to produce it. If you have a small power source to produce another power source then the outcome will be less than what you use to produce it.
Perpetual motion has never been achieved and that's what you seem to be asking for.
If you have an engine capable of producing enough energy to power a hydraulic pump/motor then you'll have less energy available to power the bike than if you'd used the small engine as the primary power source.
Yes, there are hybrids that use both fossil fuels and electricity to power a vehicle but they are not overcoming the laws of physics. There's no free lunch. You can only get what you put in. Energy can not be created or destroyed, only changed from one form to another. I didn't make this rule but we all have to live by it.
Internal combustion to hydraulic/electric/thermal, etc. The results will always be the same.
If you can overcome the laws, you'll be a very, very rich man some day. (if the oil companies don't buy it and bury it)