Nobody else seems to be addressing your question, so I'll take a stab at it. It sounds like you are considering dropping some money on an entire bass rig to improve your recorded bass tone, but you're limited to small, cheap bass amps due to budgetary restrictions. I really can't recommend that, dude.
In the first place, if you buy a GOOD bass amp, and mic it, it will sound good, assuming that you have mics that can capture the sound properly AND you have sufficient skill to know how to use the mics. But if you buy a cheap, crappy sounding bass amp (which is what you're going to end up with on a very small budget), then you're going to get a cheap, crappy tone when you record it.
Furthermore, mic'd up bass rigs aren't really used for recording all that often these days, from what I understand. About the only time that experienced recording engineers even bother to mic up an actual bass cabinet is when they have a good sounding bass rig to use (to start with), and even then, they tend to mix it in with a direct sound -- and most of the sound comes from the direct feed -- the mic on the bass amp is just mixed in to give you some of the "flavor" of the bass amp. Many excellent sounding bass tracks these days are recorded
exclusively with some type of preamp (or high-end DI) sent direct into the recording desk.
I have about a half-dozen or so bass amps and preamps that I can use to record direct with, bypassing the amp and speakers entirely. While I'm still in the process of getting my home recording rig set up, and haven't actually recorded anything yet, I anticipate that almost ALL of my bass recording will use these preamps plugged direct into the inputs of
my Presonus Firepod. I could hook up speaker cabinets and mic them (I've certainly got those, too), but I probably won't do much of that. Two of my bass rigs are able to emulate other amps (
the Boss GT-6B and the SansAmp PSA-1), much like your BassPod. While I'm not specifically familiar with
the BassPod, I should think that you should be able to get a perfectly suitable sound out of that thing.
My recommendation, therefore, is to save your money and spend more time getting a good bass sound out of your BassPod. I'm almost certain that the sounds are in there. If you're not able to get good sounds out of that unit, then the problem is probably something else, other than the preamp. Do you have a quality 'verb unit that can give you a credible room sound? Have you tried double tracking the bass to give a "bigger" sound? Maybe you just need a compressor that sounds better on bass. (I don't think I've EVER recorded bass without using a compressor of some type. Some sound better on bass than others.) Probably the most likely candidate, if your bass tone isn't working for you, is the bass, itself. Maybe you need a better bass? But I certainly wouldn't recommend buying an el cheapo bass amp just to use for recording.
Anyway, that's my 2 cents.
Brad