Welcome Coffeemamma =)
CW: you should have been riding her the day you handed them the first payment for her lease. There is absolutely no excuse that they could give you as to why there is still no saddle for her after nearly a month of leasing her.
Either she cannot be ridden or, she can be ridden but they couldn't even be bothered to get her a saddle because they see how willing you are to just hang out with her and love on her. You should seriously consider holding back 2 lease payments and getting her a saddle, (of course letting them know what you are doing.)
Have they done her feet yet? When was the last time her teeth were done? I'm very happy for you that you are enjoying each others company so much, BUT I am also angry for you because it seems these people are playing on your heart strings. I hope things work out and the next post we see from you is "I rode Belle, and we had a blast!!"
Off to work folks, have a great day