The trick to offer as little gil as possible when bidding for an item, is to avoid being caught into a bidding war. If you attempt to outbid the nobles at every turn, they will keep raising their bids and as a result, you have to pay even higher price, just because they know that you are VERY DETERMINED to outbid them.

The trick is to let the nobles bid among themselves for a while and when it seems like the item is about to be sold, quickly offer a price that is reasonable and is HIGHER than the last. This last-minute bid will most likely guarantee you to get the item at a reasonable price
There you go.