What's "light" for you? I'm a girl as well, and my Ibanez SR600 (four string) weighs in at 7 pounds 5 ounces (according to Sweetwater). To me this is pretty "light." That being said, I'm decently strong (from basketball induced lifting), so my "light" may not be your "light." It's all very subjective. If Sweetwater has basses in stock they usually list them on their "Guitar Gallery," which lists the weights of the exact bass you're looking at.
So, if your "light" is equivalent to my "light" go for an Ibby SR600/other SR bass. If your "light" is lighter than my "light" go for a Short Scale...or a Hollowbody...or a Short Scale that's also a Hollowbody. I've been GASing for the Fender Mustang basses; 30 inch scale, but Sweetwater lists a CIJ at 7 pounds 14 ounces, and a Pawn Shop at 8 pounds 5 ounces...heavier than the full scale Ibanez.
I have an Ibanez SR500 and SR600 and bought them both because they are so easy to manage. I'm 5'2" and have back problems (probably from playing a Fender Precision when I was 13 and 90 pounds) and they are great to play because they are light, the neck is very thin, and the body is shaped so that is is very thin at the edges, which cuts way back on how far you have to reach your right arm and shoulder over the bass to play it. They go for about $600, and I think the 500 is lighter. For short scales, I have a Squire Jaguar and it feels very good but is not as nice in tone as the SRs and also doesn't have as much variety of tones as the SRs. Some will tell you that the SRs are too trebly, but with the electronics on these, you can get just about any tone you want. I put flats on the 500 and can get very deep, luscious tones as well as more trebly tones.