You've asked a complicated question that will get a variety of answers. People will visualize your tank. Some will imagine a tank with plants, other will see Sponge Bob ornaments. Their answers will reflect that.
If:
your tank is already heavily planted;
your college room is somewhere where they won't turn the heat very low while you're gone;
the Betta is healthy;
the tank is a 35L/10 gallon (or at least a 5 gallon)
and the tank has a good cover to keep evaporation down and temperatures steady...
then he'll probably be fine for 3 weeks. He'll lose some weight, but if he stays at 24c/74f, he should remain fine for that period. At 2 weeks, I'd be confident. 3 is pushing it a bit, but in range.
If you transport him back and forth, then he has the physical stress of that, possible temperature fluctuations and an arrival in an uncycled tank with possibly different water chemistry. He is an air breather, so he can handle water differences slightly better. The cycling products
@f_luxus suggests aren't going to be available to you in the US, as he/she is in the EU.