How long can you go without masturbation and will you notice an increase in motivation to find a partner?

No limit. There's no requirement that you must masturbate at specific intervals. Assuming you're a man (women rarely ask this kind of question), you will eventually have a nocturnal emission (wet dream) if you try to stretch this out longer than you testicles can tolerate. Not ejaculating will definitely make you horny and "motivated, " but it may not be the best way to find someone to settle down with!