I can't easily find a left handed bass guitar. Can I restring the bass to be for a leftie (reverse the ordering of the strings)?
I think that you can do this with an electric guitar, for sure with an accoustic guitar.
Sure, of course you can. But getting it to playable condition won't be quite so simple. You'll have to re-adjust the bridge to account for the fact that the thickest string is now located where the thinnest string was, and vice-versa. If you don't feel comfortable doing this yourself (although it's pretty easy), any competent guitar tech will do it for around $25 or so.
Depending on the pickups on your bass (I'm thinking of P-pickups in particular), you'll get a slightly different sound than you would have gotten if you hadn't restrung it. This isn't a bad thing, just something to be aware of. You may also have to adjust the pickup heights, for the same reasons that you'll want to adjust the bridge.
Finally, the ergonomics of the bass will be a bit strange. Your left forearm will rest near where the knobs are, the formerly-upper-now-lower bout of the bass will restrict access to the upper frets, etc. None of this is a deal-breaker, but you may find it a bit awkward at first. If you haven't yet purchased a bass, you might want to try several different models in your preferred playing position to see if any of them feel more physically comfortable.
You say you think this can be done with electric guitar, and of course you're right: Jimi Hendrix played right-handed Strats that he re-strung, turned upside down, and played left-handed. If the greatest guitar virtuoso ever can get by playing right-handed guitars left-handed, so can you.
If everything else is OK (what the other answer talks about), you would need to reverse the nut if possible or get a new one. The larger strings won't fit into the grooves for the smaller ones, and the small strings will be too lose in the large grooves.