We lease a showpony (for my daughter) and I lease a TBxSH for myself, both from the same owner. We pay a set dollar figure each month and receive a set amount of time with the horses. There are other leasers (not many, however, the horses are not overworked) that we share with and we coordinate amongst ourselves to ensure our schedules work. It's been very easy.
We have use of the barn, each horses tack and gear, etc etc. We are responsible to clean up after ourselves, put everything away, turn everything we turn on off again, and ensure the horses and barn are secure when we leave.
We are responsible for the well being of our horses during the time that they are in our care, but outside of that time we are responsible for nothing at all. THAT is the benefit of leasing, and I appreciate the "safety net" it entails - I never have to worry about an unexpected $1000 vet bill, etc etc etc.
Bonding? My daughter has bonded with her pony quite well, but she does groundwork with her as well - just did a join-up on Saturday, for example. They are a great pair together. Me and my guy, well..hard to say on a bond - probably not a whole lot, but he does respect me which is something he challenged me on a bit at the very beginning - we got that sorted out early on. He's now well behaved and does everything I ask of him, and we must be in a reasonable good tune with each other as he seems to be able to read me well, doing what I'm thinking sometimes with only the slightest of cues. Either that, or I'm a better rider than I think I am.
Ultimately, a lease is whatever the contract makes of it though. As you can see some people are responsible for more than others, but I would expect a much higher lease cost vs what we are paying. If the lease spells out bigger financial responsibilities, you're more responsible - if it spells out little or none, you aren't - be careful with the wording and make sure that you're not taking on an equivalent amount of cost versus ownership for a horse that you ultimately don't own.