From Politifact:
Have 352 bills passed the House but await action in the Senate?
Basically, yes. We used the THOMAS congressional database to pluck out the 733 measures that have passed the House so far this year. We then weeded out a few categories of bills -- ones that, for procedural reasons, were never intended to go to the Senate (such as election of the Speaker, assignment of lawmakers to committees, and procedural motions) or ones that were subsequently taken up by the Senate (either being passed or rejected).
What remained were 342 individual bills. That’s 10 fewer than what Jenkins claimed, but we have no quarrel with her number, since the difference likely stems from additional bills being passed in the couple of days between when she spoke and when we looked through the database.