How does one go about leasing a bitch to breed to their male? What are the typical terms? TIA

I can tell you what we did the only time we ever leased a bitch. It was back to her breeder. I can't imagine I would have done it for anyone else.

Her breeder was to pay all expenses. Her breeder got pick puppy, I received the proceeds from the sale of one puppy, then the proceeds from the sale any remaining puppies was split between us.

I don't have my records in front of me, so I'll pull some figures out of the air (I think this was close).

The sale price of the puppies was agreed beforehand. So say each puppy was to sell for $1200, 6 puppies total, so that meant 4 puppies that proceeds were to be split from their sale. So total cost to lease my bitch ended up $3600. She did have final clearances and was an Optigen Normal.
Was that too high a lease fee? I don't think so, but doesn't matter because we were both happy and fine with the arrangement!

I would love to lease a nice bitch but I can't imagine that anyone would give up their girl like this. It seems that all the benefits would be to the person who would breed the litter. I am short on space here and would love to have a girl for just one litter and then return her. I can provide $$$, inside lovin' and A/C 24 hour care during whelping a raising of pups for 2 months. Excellent vet care that is available 24/7 and yet I can't imagine who I would ask to let me do this.

I agree it would be tough to get someone to lease out their bitch, especially when you know any breeding could be their last one. I can only try to explain our thinking and why we did it. First it was our girl's breeder who we leased her back to. Second, our girl's biological clock was ticking and family health crisis put showing & breeding on hold for what ended up near 2 years. Our bitch wasn't getting any younger, and hadn't had a first litter, and I didn't want her any older having that first litter if she was in fact ever going to be bred. It wasn't the right time for us to try and raise a puppy, so I was happy for my girl's breeder to get her pick from an entire litter.

Why don't they take a pick puppy back from one of his breedings instead?

Well, I would think that if someone was generous enough to lease out their bitch to a trusted person, it wouldn't be about the money anyway but about the potential of keeping that pick puppy for their breeding program.
I have leased out a bitch and was very pleased with the arrangement. I did not end up with a profit, but seldom do we anyway when things are done correctly.
The bitch had all her clearances already, all I had to do was breed and whelp her.
A lease can be a good thing if both parties can agree on terms.
I think the bitch owner really is doing the other person a huge favor and it's great when we can help each other out like that!

I don't know that it's so true that someone seldom comes out in the black if things are done correctly. I think one has to be prepared for the possibility that things could go into the red due to a a "catastrophe" of sorts, maybe even a small litter or in fact no puppies. If luck is on our side with a nice size litter and everyone is kept healthy, and all goes well, I figure break even at 3 puppies. One is hopefully my keeper, one covers the cost of the stud fee, and one covers expenses of raising the litter. Over 3 puppies, again barring problems, I would hope to end up with at least a little something to put back into the dog fund after covering all expenses.