I was under the impression that synodontis catfish usually went in tanks with african cichlids and that they could get pretty territorial/aggressive. Also, because they come from the same areas as african cichlids, they prefer water conditions that aren't really compatible with what bettas prefer. I'd stick with smaller catfish-type fish like cories.
I had mine in the following setups:
Setup one: a pair of mollies, a pair of swordtailfish (the male bred with the femail molies), 4 guppies, a school of silver dollars, 3 angel fish, a clown loach (didnt knew he was schooling at the time)a silver shark and a platy.
It lasted about 4-6 years, dont remember exactly.
After said years he was the only one left. So i changed into this setup:
3 oscar, 4 silver dollars (one remained because the oscar ate them) one platy (disappeared) one cory (disappeared also didnt knew it was schooling) one black red tail shark, and one yellow parrot fish.
The only aggressors seemed to be the oscar and the parrot which along side the synodontis were lived for about a decade.
After they expired i left him alone in the tank till he died 3 years ago after reaching 28 years of age (yep he was older than me!). He was around 17 cm long.
Anyway sorry for the wall of text but it brings me to my point: He didnt attack anything (i presume he killed and possibly ate the bottom feeders though) so i think it can live with a betta as long as he doesnt interfere with the bottom. Thoughts?