I'm using a plain old Bic ballpoint (biro) pen and I need recommendations for drawing paper(s) with tooth, but without a 'pattern' like charcoal paper.

I've tried hot press watercolor and bristol paper, but neither have sufficient tooth. Mixed media paper didn't cut it either.
Cold press watercolor paper was too bumpy.

Stonehenge or Lenox have juuust enough texture to grip the ball point but not enough so you can’t have a smooth line. And visually won’t interrupt.

As Jalen mentioned, Stonehenge and Lenox are the two top papers we'd recommend that have smooth surface texture with just enough of a tooth to grab the ink.

Some additional papers to round out the selections would be:

Somerset Satin
Arches Rives BFK
Coventry Rag Smooth

All the papers mentioned above are 100% cotton. Here are links to the respective product pages:

https://legionpaper.com/stonehenge/
https://legionpaper.com/lenox-100/
https://legionpaper.com/somerset/
https://legionpaper.com/rives-bfk/
https://legionpaper.com/coventry-rag/