Bettas not only breathe through their gills, but also by coming to the surface and breathing through their labyrinth organ. Because of this, the bubble strips aren't necessary, and may make swimming more difficult for them, especially the male. Your plans, if live, will also do better without the bubblers. A standard HOB (hang on back) style filter that would usually come with a 10 gal tank will provide enough surface agitation to adequately oxygenate the water. You don't necessarily have to remove them, but in this scenario, I would.
Unfortunately 2 plants will not provide enough cover for the fish. The tank should be heavily planted and/or have lots of decor so they can stay out of the eachothers site when necessary. Tall plants and floating plans would be good, since they are surface breathers.