If I place multiple bids for different amounts, will the winning bid be the one that comes the closest to the next highest bid?

The highest bid amount will be deducted if you win the claim, so there's no need to place multiple bids for the same player.

Example If Team A places $2, $5 and $10 bids on Player X, and the next highest bid is $4, Team A will be awarded Player X and charged $10.