The highlighted words are antonyms, so each bidder will be buying letters to create words that are opposites. The story line says that the man in the top hat should get his letters first, and the baker (the lady with the open umbrella) should be the last to go.
The hints given say that one must try to get rid of the bidders, one by one, until only four letters remain.
There is a certain order that will need to be done for this, since some bidders are likely to snag letters meant for others. Play around with the order until you can get the right pairs to the right bidders.
Once four letters remain, change the strategy a little to keep both bidders out there as long as possible. After all, more bidders means more gold.