Remember that once you put a player on sale, you have around 1 - 2 hours, that's way more then you need and you don't need more then a browser opened at a time.

This tactic is actually no secret and very popular among the old players who took over new clubs.

There's also the possibility that somehow with few hundred tokens started to bid for X player few hundred times so you can also do it from one account. Is a better tactic then buying directly from the bank.