A form of the word "Bowser," referencing, of course, Bowser of the Mario series. The expression is colloquial to Middle America, particularly parts of rural and suburbian Iowa. However, small patches of society in southern Texas tend to use it sparingly.
Bowsah is primarily used to describe something that is particularly difficult, comparing it to being the "final boss."
Another usage is to express something particularly nasty or rude in terms of societal perceptions.
It is also used to describe something that is annoying and recurring, as Mario had to fight Bowser a buttload of times and yet always seemed to triumph over the larger, stronger freak of nature.
Guy One: Man, I'm having such a Bowsah time filling out my taxes. They're being very Bowsah with me down at my tax agency.
Guy Two: Yeah, it's the same Bowsah crap every year. Tell you what I do, I give the Bowsah attitude right back to them.
Guy One: But won't that make them angry and increase their Bowsocity?
Guy Two: If you have to deal with a Bowsah kind of person, don't you want to be their Bowsah, too?
Guy One: Bowsah.