Interesting... this is something I LOVE, because I LOVE filters.
I think what you're looking for is probably only found in a higher end envelope filter. 75% of the envelope filters only cater to that funky sound, since it's what 95% of the users want out of an envelope filter. Most filters don't give you many options to get away from a funky sound. The better ones do.
Ok... Let's look at what makes those envelope filters sound "funky" or "whacky." The "whacky" sound is made a few things. First, it's made by a pretty high "Q," resonance, intensity, or one of several other descriptions on how tightly the higher frequencies are cut off and receive a slight boost just below the cut-off of frequency. Next is the frequency range of the filter. The "funky" or whacky sound is made with a moderate-sized frequency sweep over the mid-ranges of the bass. The bass on the song in my signature (as of today, I'll change it later) has all these settings on it, and I think it sounds probably exactly what you're NOT looking for.
Lastly, the cheaper envelope filters often have two hard-wired settings that aren't changeable, but lend themselves to a "funky" sound since that's what sells. One is that the frequency sweeps are only set to "up" sweeps, where the harder or louder you play, the more the highs come through. A "down" sweep is usually an option on better filters, and won't sound quite as 'funky' (although it can). Also, the attack and release of the filter is set usually to moderately fast to give the bass that bubbly sound. Higher end filters can be set to have a very fast or slower attack, both of which will move away from a funky sound. Also, changing a release speed away from moderately fast will make it sound less funky, too.
With a higher end filter, there are a vast number of sounds you can get that won't sound typically "bubbly" or "funky." It just takes a bit of knowledge to coax them out of the pedal. Additionally, they may have multiple frequency sweeps, which add a totally different dimension to the sound.
As such, if you start messing with settings that DON'T follow one or more of the sounds typical with funky envelope filters, then it won't sound as bubbly. For example, a moderately slow filter with the frequency sweep set fairly wide from mid to high on a "down" setting, it will NOT sound bubbly or funky.
The bottom line is that filters are crazy fun with a ton of options, if you get the right pedal. You're probably looking for a higher end one, and you just need to move the settings away from the typical ones set for that "funky" sound as I described. It can be done, but just read up on what envelope filters do, and then forge away from that funky sound.
Also, I always suggest tossing a bit of overdrive or fuzz before the pedal in the signal chain. That really brings out the filter's effect more dramatically. When trying out pedals at the guitar store, I strongly suggest getting the salesman to put a OD or fuzz pedal on the bass before the filter.
Good luck, and happy hunting!