bamboo is not an aquatic plant, leaving it in the water will kill it eventually and foul up your tank.
really, it's not even meant to have the roots in water. to be healthy it needs soil, very moist soil.
I'd suggest removing it and getting something else. avoid mondo grass too, that's another non aquatic plant commonly found in pet stores.
unfortunately not, don't just trust everything pet stores say. they sell goldfish to people who plan on putting them in bowls. they sell oscars to people with 10gs. pet stores are RETAIL stores just like every other store. their goal is to make money. people buy bamboo because it is asian and bettas are asian so they think it is perfect for their betta bowls (don't even get me started on that...)
anyway, what I'm saying is ALWAYS do your own research.
I'm just telling you the facts. they won't last submerged, they are not aquatic plants. take it or leave it. keep it in and find out yourself, you're not spiting me. just trying to help.