I agree with djembekah: Dwarf shrimp are great (I have 80+ in a divided 20 long with three Bettas).
However, I feel like a broken record.
To be successful, the tank must be mature (cycle completed for at least two months). There must be lots of cover which means a heavily planted tank with live plants. You have to buy shrimp food or break up algae wafers as they won't eat Betta food.
You could try an Amano, too. They need lots of cover, too, but have great personalities and you can keep them with dwarf shrimp.