Both diluted bleach (plain Clorox from the supermarket) and hydrogen peroxide are fine for cleaning personal enema equipment at home. But keep in mind that the tubing is more likely to become contaminated with mold than the bag itself.
It is especially important to allow the bag and tubing to air dry throughly before putting away in a drawer or closet. Hang it on the back of the bathroom door, a hook on the wall, or on the shower curtain pole for several days after each use. Make sure the tubing isn't looped more than once while hanging so water can't pool at the bottom of a loop.
It's also not a good idea to share your personal enema bag with other family members, but if you do, make sure you disinfect the equipment thoroughly after each use.