I'm thinking that the bag was open at the bottom when Teller stepped in. He stays upright long enough for us to see that his head is in the bag, then quickly crouches, pops under at the bottom, and seals the bag after himself.

He tugs gently on the bottom to remain hidden, and so the guy holding the string doesn't notice the weight change.

We never get to see the bottom, because the lights are still too dim immediately after he is revealed.

The helium quickly lifts the bag too high for us to see the bottom, but it does have a sort of heart shape at one point, suggesting a seal in the middle of the bottom, rather than the straight edge a factory-made bag would have.