How could it have been any clearer: Only Jane Jones' name was on the wedding invitation's outer envelope. It was also the only name on the inner envelope. How come she interpreted that as license to add a plus-one to her response card? Either Jane was being defiant or her knowledge of basic wedding etiquette is seriously lacking. What's a bride to do? There are a few ways to deal.
Option A: Say nothing and let her bring the plus-one.
Allowing her to bring a date—without addressing the situation with her—will save you from having an awkward conversation (or an argument). While Jane will be happy, other singles will not. Be prepared for those without plus-ones to be upset that Jane got to bring a date when they didn't.
Option B: Tell her no.
Call her by phone and say how happy you are that she's coming to the wedding but that, as much as you'd like to allow dates, you have to cap the guest list at a certain number because of budget or space limitations, and that means the invitation was only for her. Don't be accusatory or argumentative—maybe she hasn't been to many weddings and thought plus-ones were the unspoken rule. Be kind but firm. Unless her plus-one is her husband or longtime partner (but you would've known that), stick to your guns. End the call by saying you hope she can still come to the wedding.
Option C: Let the rest of the singles bring a plus-one.
You could reconsider your rule. Is there enough room at the reception venue to accommodate more people? Can you revise your budget to pay for the extra dinners? Would it bother you that you might not know many of the plus-ones at your wedding? Keep in mind that you shouldn't allow some singles to bring plus-ones and not others—this is an all-or-nothing situation.