I bid on a few minor leaguers during free agency, but even when I offer a STI and NTC their agents say, in about ten different ways, "Other teams are offering more money." These players are decent Low A players, but I can't believe anyone is offering a BL contract. When I try to add to the salary or add a bonus, I get an error message, "Error: A minor league contract will default to 1 year for the player's minimum required salary. No bonuses are acceptable." So how am I getting outbid and what can I do about it?

It also takes into consideration your depth chart at that position.

You've got owners in your world who don't sign their draftees and/or don't promote minor leaguers. Their minors are bare so they backfill by signing any and all of the cheapest free agents just to fill out their rosters.

You aren't getting outbid. Minor-league contracts are set in stone: 1 year at whatever money they are asking for. As dschang said, it will take into account the depth of your team and any other teams pursuing that free agent. Spring training invites might help a little, but it really comes down to organization depth.