I think it may be an actual ticket, likely to one of the Balls in Bath. About a decade after the setting for NA, but likely still valid - The "Rule & Regulations" for the New Assembly Rooms at Bath, November 1816, included (in reference to Dress Balls):

"That a subscription of 1l 10s. to the Dress Balls shall entitle the subscriber to three tickets every ball-night; one for the subscriber, not transferable, and two for ladies. These two latter tickets will be transferaable, on being endorsed by the subscriber, without which form the bearer will not be admitted. A subscription of 15s. shall entitle the subscriber to one ticket, not transferable."

There are other references to the less formal "Subscription Concerts", again with restrictions as to transerring the tickets (usually only to a "lady").

To be non-transferable, I would assume the subscriber's name, or designate, would have to appear on the ticket. Perhaps Catherine is thinking how much better it would be to have "Mr & Mrs" in front of the name on the ticket, rather than depending upon the kindness of another to write "Miss Catherine Morland" upon the paper.

I remain,
Jason E.