Big Mal: How 'bout "My bodrhan, my bodhran. a strap for my bodhran!"

Can't say I've ever seen a bodhran held in place by a strap - but what a great idea!
If i were to attach onr to mine, i'd probably either do as one suggested and adapt a guitar strap and attach either end of the support dowel(s) or (rather than screwing something unsightly into the body, try drilling a hole close to the underside rim (away from the skin) and attach a lanyard or guitar strap with a miniature Carabiner (Y'know - those things used for abseiling and rock-climbing) it would be secure and if coloured (anodised) could look quite stylish. Dunno where you'd get one overseas (Britain or US) but we have "outdoor adventure - type stores over here in Australia (Anaconda and Kathmandu come readily to mind)- you'd probably find one with a colour that would match one of those in the design on your bodhran-skin (if you have one).
I'm certain also, that you could find a really nice guitar strap with a cool Celtic design on it to complement your bodhran as well.