I'm left handed and just play right handed. It worked well for me. I found that starting out my fretting hand was a quicker learner than my plucking hand. This is partly due to my negligence to work on playing with fingers a lot back when I started and possibly also being left handed... To this day I still prefer a pick but that's besides the point.
I tried learning left handed (after already playing right handed). For this I strung the bass like a left handed bass. I think you'd be putting yourself as a disadvantage by playing strictly upside down. If you're going to play lefty, I'd string it lefty (you might have to file the nut... I did) and then get some cash together and get a true left handed bass.
There are great players who play upside down, I just feel like it might be an unnecessary hurdle you'd be able to avoid by deciding to play strictly left handed or right handed.
I'm sure a bunch of our other lefties here can throw in some great insight too.
