and thanks for asking.
3 gallon is quite small, are you able to upgrade to a larger tank?
How long have you had your Betta, and do you have a picture?
I have Cory's, Kuhlis/Java Loaches, Ottos as my "clean up" crew, but my tanks are generally larger than yours. Have a look at Corys, they are wonderful little workers but you would need a larger tank to house them. Panda Corys are cute and stay fairly small compared to some of the others.
Hopefully with a Betta it should only be fed small amounts and generally will eat what you give him/her straight away.
NB: no bottom feeder will make up for how often you do water changes, and the smaller the aquarium the more you have to do them, you may even need to do yours twice a week. Just taking out a couple of jug fulls of water and replacing them helps. If you think about it in the wild the water is constantly replacing itself whereas in an aquarium, especially a small one, the water can soon become stale from the waste the fish produce. Also, by adding bottom feeders you are increasing the load on the aquarium and filter so it would not reduce the water changes but increase them and in your small aquarium this alas is not possible.
Can you put your location in your profile as it assists in advising you, as different Countries have different equipment etc.
Hope this helps.