It really depends on the personality of the betta and the frog. I have a female ADF in with my male betta in a 3 gal and they do fine...for the most part; they just ignore each other. They DO, however, compete for food and the betta tends to get the better of it since the ADF is a much slower eater. The ADF doesnt get to eat as much as the betta, which has caused my feeding to be much more difficult since I have to supervise and intervene with the turkey baster. Bettas dont know when to stop and can die from overeating and Shogun (betta) will continue to try to eat Zen's (ADF) food even after he has already probably had too much. I would not recommend getting a long finned betta since my female ADF does have a tendency to view his flowing fins as prey and latch on to them every now and again, which results in occasional torn fins. Also, even though the ADF's themselves have a low bioload, they are messy eaters and you will have to work to keep the leftover food from becoming both water fouling and betta food. I do half gallon water changes every other day.
I have read that some bettas will attack and kill an ADF, though... It really just depends on the personality of your fish. Some bettas can have tankmates and others need to be alone.
Something else to consider: ADF's need lots of cover. While they can have great personalities and do lots of funny stuff, they also can be boring a lot of the time, either hiding or just chilling out. I've found the best way to enjoy watching Zen is to provide lots of floating plant cover so that she comes to the surface by the glass. Also, they are fast. They can and WILL make lunch out of fish smaller than them and are much less active and hide much more when kept with fish same sized or larger than them. Keeping them with a betta, while interesting to watch them interact, is probably not the best way to keep them. I will, eventaully, be getting Zen her own environment because I think they will both be happier that way.