I was having the same problem a while back. I run it through a guitar POD now and it has a compressor on it and its giving me the punch I need. I usually use the British classic setting, at least that's what I think its called. If you don't have Pod, you can run it through a guitar amp, you'll get more presence than running it straight to a recorder or even a preamp. I'm assuming you have some sort of guitar amp. You don't even have to run it through the speakers, you can run it through the line out or the preamp out.
If you don't have a pre-amp out on your guitar amp then you'll have to run it through the speakers and mic it. Do so at a low volume so that you don't blow your guitar amp speakers. Record the bass with a little more presence, or a little brighter than you think it should be, you can always add bottom later when you mix. This will give you a little more of what you're looking for.
If you don't have a guitar amp either, then the only way your gonna get more midrange is if you either, hit the strings closer to the bridge or use a pick to play your basslines if you're not already doing that. And if you must go straight to the recorder with it, yeah, get new strings, thin ones, this will help......Ray J