The U.S. has a bicameral legislature and a presidential veto, so the House of Representatives would also have to vote for the same bill, then the president would have to sign it. According to the text of the bill[1], it would take effect immediately, but there would be no practical effect until November 6, when DST is scheduled to end.
True, that's the normal process but if the President vetoes the bill Congress can override the veto by 2/3 majority in both chambers.
IIRC the Senate passed the bill unanimously. If the House passes the bill by a large majority it predicts a veto would be overridden. In such cases even if inclined to veto, the President typically acknowledges defeat and signs the bill into law.
[1] https://www.congress.gov/bill/117th-congress/senate-bill/623...