We played Palazzo as a 2 player game and if the other player is not interested in bidding, do I get the floor tile for free? Seems I should have to spend something since I had to bid 3 initially.
That certificate is "yours" when you open the bid with it. If no one offers better then that is the only thing you have to "pay". Done (and that holds true no matter how many players).
The player whose turn it is, begins the bidding by placing the value 3 certiﬁcate in his play area. This is his ﬁrst bid. He may not bid more than this as his starting bid*.