MMB can show details of a booking that has not been ticketed. Without a ticket you are not actually going to be able to travel. BA can take a long time to actually finish issuing a ticket when you change your ticket, but you cannot hurry them until within a couple of days of departure. Keep an occasional eye on the situation, in particular use the mobile app and look for a ticket number in the details or try the 'Print/email e-ticket receipt" option on the web interface. If you still don't see a ticket in week or two's time, call up to ask why; be prepared to supply payment details again (especially CVV).