If you want multi-journey, rather than multi-day, use the bus, which of course has 100% checks on all journeys. Buses officially only take bicycles on vehicles with boots, though.
I have no idea what tickets are available on Ulsterbus (website helpfully says "phone us") but I don't believe that non-time limited multi-journey tickets are available outside the Metro system. Ulsterbus has only weekly and monthly tickets, or the wonderfully ridiculous iLink system which places Donaghadee in the same ticketing zone as Enniskillen, and which is therefore wildly more expensive than anything else.
In any case, a bus from Donaghadee to Belfast takes around an hour. There's an express morning service which takes 5 minutes longer than that. I'd prefer to drive to Bangor and get the train, but Translink and the Roads Service are actively making it cheaper and more convenient for me to drive, despite the fact that I would LIKE to be using public transport.
I did tweet Translink yesterday to ask, with the response that "unfortunatly non-time limited tickets are not available - please contact NIR". If it is "unfortunate" then (a) fix it and (b) I've contacted "Translink" and they refer me to contact someone else. You'd almost think it wasn't an integrated transport company.
In other news, the lane markings at the Cromac St end of Oxford street have been altered to fix the issue I raised before (which lane for straight on, outside bus lane hours) however there's still confusion on the turn into May Street.