yo dawg, i heard you wanted a solo public session so we put a public solo on your public sessions:
make a playlist
add 1 race with a short lap ('criminal damages' is popular)
call your playlist something stupid
anytime you want to make one, play your playlist single race 1 lap (its fastest). You can race solo or with anyone you want to join your solo public, they just have to copy your final steps (players do this because if you game invite buddies in, it tends to increase rando joins)
MOST IMPORTANTLY:
when you finish, hit like/dislike it doesn't matter
you'll see a final end-playlist screen with the option x to restart, a to continue --
everyone hit x, wait a few seconds, then hit a. The screen should show your vote to restart change to 'continue'
wait for the playlist to re-open the race lobby settings for inviting friends, then back out with b
it will dump you in a public lobby by yourself.
stock/sell product until randos join, then repeat
works for xbox 1, i'd wager it works on most