I've had a half-dozen ShurGrips on bows and for your stated purpose they may be the best choice. They are actually much thinner than most inner tube, they look/feel better in the hand, stretch better and are much easier to put on a bow unless your particular bow has a very narrow riser. I've mounted them on Widow MA recurves (fairly large risers) and similar bows by rolling them up the limbs into a 'donut' shape and using a piece of cord to help stretch the rubber over the high spots on the riser. Can't easily do the larger risers with innertube.
Maybe the best overall grip material is good ole' leather. It is available in inexpensive scrap pieces, many colors and thicknesses, it's functional, non-slick if mounted with the rough side out, and fairly easy to lace on. You don't need adhesive if you lace them snugly, making changing/removal easy (and protecting the riser wood form glue marks) if you decide to replace them later.
Also, there's something to be said for a bare riser (i.e. no cover). It's one of the best ways to make sure that how your hand is contacting your particular bow is done in a way that minimizes bow torque, which can cause accuracy problems. If it's 'slippery' (such as when wet or sweaty) the bow itself will often tell you how it wants to be held to avoid twisting. If your bow tends to move sideways in your hand when shooting, you might want to look at how you are holding it as a way to help correct any torque problems that might be present. In that case you might not even need to cover the grip.
Plenty of choices to consider.