Do I get my gold back when I make a bid in the Auction House and it fails?
Yes - you'll see the amount you bid present on the "Completed" tab if you are outbid, and will have the option to "Return to Stash".
You do get the gold back. When a bid fails (usually due to the item being purchased by another player) or you are outbid, the gold goes to the Completed tab.
Sometimes the gold will not appear there right away. If you successfully complete another purchase or close/reopen the Auction House, all your failed bids should be updated.