I tried the betta bulb plants from petco and they didn't grow but got moldy instead
SO i got some amazon swords and water wysteria instead. They were buy 2 get one free with a petco pals card. So far, they do pretty good and I do not add anything special for them to the tank, just give them light. I like the wysteria because you can float it in the tank and the roots will grow downward from the plant. It gives the tank a more wild look and the betta loves to rest in them. But do be careful as to which plants you get, because as greentea said many of the plants petco sells as aquatic are not real aquatic plants - they are bog or marsh plants -
the bottom is under water but the leaves are above water. Bamboo CAN work but it has to be tall enough that the leaves are not underwater.
Personally, I would be on the look out for floating plants. Eventually they will go on sale again. I think floating ones would work good with your setup as the top of the tank is empty and they will give the betta something to rest on near the surface :D
Aquatic stuff is $$ here, so I slowly add things to my tanks. If you have an ebay account, sometimes you can find live plants or decorations for cheap