Neon tetras, from what ive heard, are generally a bad choice to suit to a betta as they have been known as fin nippers, and also the fact that your betta might eat the tetra should the tetra be small enough. Apparently the best companion for a betta is an otocinclus/bristlenose catfish/corydora as they keep to their algae and will not disturb your betta.
Hope that helps