There is no bid system. Per league rules, whatever is agreeable to both players may be done.
A single secret bid is faster and easier, and can be interesting because you’re not bidding off of each other. If you don’t like that idea, then why don’t you tell Juan how you want to bid?
If you two do actually agree to do a single secret bid, I can receive it and tell you who won, yes. Fine with me if you find someone else too.
But again, as the league rules state, the starting set up (including bid) should be agreeable to both players, so you guys need to agree on how you’re going to do it.