Try the JPTR jive. It’s the only ‘bit of hair’ that ever actually delivered on that promise for me. It makes my bass sound just a little fat and gooey with a hint of a wet cough (in a good way.. like a good wet cough when your sore throat starts to clear up).
It gets plenty dirtier than how I use it, it sounds great with fingers, where most pedals just get farty. And it’s super inexpensive. it also doesn’t just make me disappear in the mix like most dirt pedals.
Darkglass stuff just sounds sizzly and scooped, a lot of ‘tubey’ stuff just doesn’t deliver for me, and most other things either fart or sound like a Distortion+
I’ll recommend the Jive every time, and even moreso for what you’re describing.
That said, for what you’re describing, I personally would use a litttttle reverb or a hint of slapback. Bassists run from that stuff, but used sparingly, where you’d almost not notice it until it’s turned off again, it can REALLY add some dimension and dimension to your sound.. I don’t mean to get carried away, but when I’m in a power trio and I need to fill the space when the guitar switches away from heavy chords but we want to stay big, I’ll use some kind of octave- either a polyphonic like OC3/5 and play double stops with a fat octave underneath, or else I use a (heavily modified/eq’d) octave up, an octave fuzz, or a reverb with shimmer (octave up on the reverb)
but if you wanna keep it simple and just add a little body to the mids and a patch of hair, go with the Jive!