The house has to pass the bill first. It hasn't even had it's second reading yet.
Then it goes back to the Senate. The Senate may agree with, or disagree with the change. I presume this will require a discussion and vote. If they accept the change, the bill moves forward. If they refuse the change, the House and Senate would need to appoint a commitee with a few members (3 from each I think) to negotiate an acceptable bill which would require another vote in each body. If they fail to reach an agreement on an acceptable bill, we get to wait until next year for another shot.
We all know how much time was wasted during the initial discussion of S 308 in the Senate. Like I said, I haven't combed over the rules in detail, but I know of nothing to prevent the same anti-gun Senators from discussing the same inane nonsense again. The clock is ticking and the session is over in two weeks.