i just want to add something to callistra good advice. I would do 2x50 and 1-100% water change like callistra said that some people recommending it. Also make sure you leave space between top of the tank and water level as bettas are very good jumpers. It a lot of accident with bettas jump out. The same when you changes him or take out of the water be careful. I had accident also when one of my betta jumped while i was changing it.
If he is not eating but otherwise is active and don't have any visual symptoms on the body then he just adjusting to the new environment.
I agree take the filter out. In the small bowl you don't need it since you will do 100% water changes, and also i think it too much water movement will stress him out.
Also people get crazy about temp 76-80* is the perfect for bettas. I have my bettas in 74-76*. The warmer is the temp the more chance for infections. And also make sure you take out all uneaten food so it will not contaminate the water.