I can't even remember how I ran across the Ashbory bass, but it's a pretty remarkable instrument. With an 18" scale (compared to a standard bass at 34" or a Stratocaster at 25.5") it's the most compact bass you can imagine. But with it's unique silicone rubber strings, it has a rich, upright bass sound. It requires a different style of playing due to the fact that it's fretless and, of course, given the shorter scale. While it's not likely as easy for a beginner to learn as a fretted bass, it's a heckuva lot more portable and weighs only 2 pounds.
The original design dates back to 1985 when it was invented by a couple of brits (Ashworth and Thornbory) and was previously marketed by Guild and later DeArmond. Now Fender owns the brand and you can order them on the web and see them on eBay routinely for under $300. Brock Frazier's web site www.largesound.com has a ton of information on this unique instrument and also sells them for around $250.
I picked up one of these recently on Craigslist, and while I'm not a bass player, it seems pretty wild. It weighs next to nothing and is by far the most portable instrument I own. It may take some time to figure out how to play this thing, but its pretty cool looking and has a very rich sound.