First off, you may be confusing amps, and amp hours. But for sure, the bigger your battery in amp hours, the less amps each cell has to put out, to supply your controller with 20 amps of current flowing. In addition, your pack may have a bms which limits amps to 40, or 60, or whatever, in case you hook it up to a very large amps controller at some time. In general, for a 20 amps controller, a 40 amps bms will be plenty. At first start, it will pull more than 20 amps for a brief time, and you don't want it shutting off before it can get going.
Your controller will max out at or near 20 amps after that first spike at starts, The motor will gladly suck more, but the job of the controller is to control that, limiting it to 20 amps. So it quickly ramps the amps back down to 20 or so. This is partly to limit speed, or power to legal limits, partly to make motor burn out less likely.
So yes, make the battery as big as possible, without making it too heavy and awkward to carry on the bike. 15 amp hours of 36v will still be pretty light and compact, but 20 ah of 36v can still be carried easy enough.
If you want huge range, then you need to carry a lot more, and in general, are best to consider cargo bike of some type, which is able to carry 30-40 pounds without handling poorly.