First of all, shorter bows are generally preferred as they are easier to maneuver with when on horseback.
Second, you’ll want a mounted archery bow with a good draw weight for you (Draw weight refers to how hard it is to pull the string back). The higher the draw weight, the faster and further the arrow would go, but the harder it will be to pull.
For reference, I’m a young adult, female, with little to no upper body strength and prefer my 20lb bow. I also have a 28lb and can pull it, but I will tire out quickly when using that bow and can not fire it as quickly (which is important for mounted archery). However, I wouldn’t go below 15lbs for fear that you might start struggling to get your arrows to reach the targets.