How to clearly display automated auction bids

I am currently working on a small Auction site. On this Auction are items and on the item's "Details" page displays a list of bids on the item descending from the amount, so the "active bid" will be at the top of the list. The bidder clicks a link to a form which in they can put their max bid.

The problem I am facing is that the customer I am creating this site for would not like the bid list to show a user bidding twice in a row which would happen in specific use cases if you showed every bid increment.

Let's say I have an item with a starting price of $100 and the bid increment is $10. And Person A places a bid with a max of $150, so Person A has the current bid at $100.

A second bidder Person B bids on the auction and has a max of $200. So normally I would imagine the bids would look like:

5/23/18 8:30am __________Person B___________$160
5/23/18 8:30am __________Person A___________$150
5/23/18 8:30am __________Person A___________$140
5/23/18 8:30am __________Person B___________$130
5/23/18 8:30am __________Person A___________$120
5/23/18 8:30am __________Person B___________$110
5/22/18 4:00Pm __________Person A___________$100

So in these specific cases where it would be an odd number of increments away either person would have to bid twice in a row, however my customer doesn't want any confusion.

The code I have below I try to address this issue by creating special incremental bids. The output of my code in the same case would be:

5/23/18 8:30am __________Person B___________$160
5/23/18 8:30am __________Person A___________$150
5/23/18 8:30am __________Person B___________$110
5/22/18 4:00Pm __________Person A___________$100

However, I also believe this sparks confusion as the bidders may ask why the price of the bids jumped. Also with the code I have now I believe that I would have to further split my if cases to account for if a bidder were to place a max bid that is one increment higher than the current max bid.

How should I present these situations to the bidder in the least confusing way?