One of my projects of late has involved recruiting board members for a state organization. There are various requirements, of course, as well as a potentially complicated confirmation process but I've still been surprised by how difficult the job has been. Fortunately, I've had a very good team and so the burden hasn't fallen completely on my shoulders. The others have encountered the same challenges.
The adage that if you want something done, ask a busy person contains much wisdom and yet there is also this hard fact: busy people know how to say no.
I was just lured onto yet another board and so know the emotions. You can feel noble if you say yes and liberated if you say no. The exhilaration of liberation lasts longer.
Either way, keep reminding yourself that it is an honor to be asked.