Hi Jörg,
thanks for your reply.
OK, let me give some background to my question.
I'm mainly a guitarist, happen to play in a bigband.
Three years ago our bassist (BG) dropped out, and I took over the bassists seat, starting with DB, as I had some weeks preparation time to build stamina.
(I played cello for a bunch of years, so the technique was adoptable.)
I paused playing for 18 months now, cause I was very busy and did not have the time to keep my fingers trained,
and changed to BG.
Now I want to get back to the DB, as it is more fun.

I have inherited a astonishingly good sounding cheapo bass,
use a Fishman Cello pick up (P-100) into my trusty AER Compact 60, which worked OK with the 3MOhm Input,
which I now upgraded with francis HPF-Pre to 10 Meg, which is a huge win and works pretty well now.
So,
Lavaliers are made for speech. So they are far from being linear.
My Setup as above, what bugs me most is the weird sounding string handling noise, which is overtly loud and in your face with the bridge piezo.
Also it is too direct, in time domain, as opposed to acoustic or mic'ed bass, in my ears.
Now, I have no parametric at hand, but I guess this string noise happens at about 1,5-2 kHz,
which is right in the spectrum of a lavalier.
I get enough fundamentals from the Fishman and the HPF-Pre, but for gigging some less fake overtones would be cool.
If you have a look at the anthem guitar pick up by L.R.Baggs,
they have a mic and an under saddle transducer and a crossover at 200 HZ.
I have no Idea how they got away with that without audible phasing,
but for a similar bass setup one could use a pick up, a small mic that does not have too see too much LF to reduce feedback inclination,
and an electric PU with a lav would be a small, unobtrusive and elegant package.
Cardioids are not the best soundwise for nearfield double bass pickup, a uniform or hypercardioid characteristic sounds better. So for recording, I would prefer these types, for playing live the cardioid types might reject a little bit more of the surrounding noise and feedback than the uniform one.
I can't see anything but feedback hell coming from an omni on stage.
Hypercardioids seem difficult to get as lavaliers,
on a quick search.
Did you read about the special DPA 4099 for double bass and the AT 350 and AT 35 Pro?
Search the forum and read what they can and can't be used for.
I got it on my wish list,
as it seems to work really well on guitar as well (
Utube) and it is polka proof (
Utube as well)

It seems to be a shotgun design though,
which makes sense, feedback wise.
(There seem to be different versions with different sensitivities or different bass roll of, iirc,
I'll check that before ordering.)
But this has to wait a few months...
Magnetic PUs and microphones are on opposite sides of a scale of recorded or pickup sound.
Yep,
but they should complement each other quite well.
All the best,
Bassmensch