Can I pay someone else to operate a miner on my behalf? Is there a company or individual out there that sells Bitcoin miners and holds them under their supervision for a fee? If so... I'd like to know.
There are lots of them, that's called "cloud mining" - just google the term and you'll probably find your way.  You either rent a miner or pay for mining equipment, or eventually just throw your money into a black box with the expectation that you'll get some reward later - basically mining operators crowdfunding some (or all) of the investments and associated risks.

Be aware that some "cloud mining"-operations have been nothing but ponzi scams - no real mining equipment involved, just a pool of money with early investors receiving fantastic payouts from the pool, and eventually the operators grabbing the whole pool and running when the inflow of new investors no longer can offset the payouts to the earlier investors.