One lesson a month is something but im sure you would want to do more than that?
Before I bought my own horse I rang around and found a woman with some horses who was just going into dealing them. She asked me to go and meet her which I did and I was there for about 5 years riding all the different horses she got in.
I got to ride all kinds of horses and learn everything I needed to know about owning one myself!!
We are still very good friends 7 years on and if I ever have a query I go to her and she helps me choose horses when im looking for one to buy!

This gave me the opportunity to ride everyday and help out on the yard!
Another option would be to call a riding school and explain to them that you want lessons but would you be able to help out on a Saturday of something in exchange for a ride?

Places everywere offer that because they dont have to pay anyone that way

Hope this helps!!