It should be ok, but I can only guess in a general way at it.
find out what amps the controller is. Likely 20 or 22 amps. Then match that with a battery that lists its max amps at 30 at least. In most cases, even the cheaper cells out there these days can handle 30 amps, in a 10 ah size battery. Then, with 30 amps possible, and 22 your max, you should be fine for the battery to last quite a while. However, a battery listing max amps as 40, with your controller only 22, should have an easier life, and perform better for longer. Good cells can be worth their cost. Or go bigger with average cells, and get the same 40 amps max.
If your range will be a bit short on a 10 ah battery, ( figure on one mile per ah riding fast) then get a larger battery. Bear in mind, just because you have enough range when the battery is new, doesn't mean you will by next summer. So if your ride is 8 or 9 miles, you'd eventually need to slow down some to make it. Figure on 2 miles per ah if you only ride 15 mph. IMO, the real reason to go big is to increase your ability to go far on the bike, and leave that car parked more. I tend to never leave the house carrying less than 20 ah, and often carry 33 ah.