Probably $500-1000 if you hire an electrician. I did it myself fairly easily (largest cost is the copper wire if it's not a short run; GFCI breaker can also add a little cost if you have to have one - it's code in some states)

Many states or municipalities require conduit for >=110V. Some require licensed electricians to perform all work, along with permits and building inspector approvals. Yes, even for pulling a new circuit from an existing panel.