The Doctor was thinking, he knew that Elemmire was scared, He knew he couldn't leave her there, He knew that he needed to keep bidding, at least until he won and could get close enough. He wondered how high people would be willing to go. He then bid $ 500 000 000. If the others went higher so would he. He wasn't backing down till he could get closer to free her, He had his sonic screwdriver close by , so he could use it to break her chains if needed to. He wasn't sure if they would break the once he gave the highest bid.

Once the Doctor was able to get closer, he broke the chains with his sonic screwdriver, he was doing it carefully and made sure nobody knew what he was up to. It seemed the bidding was going on forever and he didn't seem to know what would happen if he didn't try to free her. He was making sure that the plan was going to work. He knew the TARDIS was close as well.
[i] Run , when you see a blue box go inside it [/i} the Doctor told her, He was ready to run as well. He knew they would have to be fast to catch up, he was going to make sure that didn't happen.