That sounds good my friend!
But, do try to work your exercises so that you also strengthen the muscles in your upper back between your shoulder blades - I don't even know what they are called, but they are very important in drawing the bow - you don't want to have it all in your arm and outer shoulder. It is harder to isolate those, so sometimes one just has to do what you can. Exercises with a dumbell that might work that area could be something like back flies with a dumbell in each hand (start light) or bent over at waist (brace head against wall if necessary) and pulling dumbells straight up to chest (near breastbone) and also doing the same but far apart (to shoulder). Try to do as many reps as you can without going really fast and feel/try to isolate the different muscle groups - again, you want to strengthen without ripping something. A rowing machine or an old fashioned rowboat aren't bad either! I'll do some pushups, too, but the exertion force is kinda in the wrong direction, unless you work on going down to the floor slowly, or something.. just doesn't work as well.
