Yes there are asteroids bases (32) since version 2.2. Most of them are in nebulaes around bubble.
Each of them is dockable with refuel, repair restock service. Some have also outfitting, and some have shipyard.
The DSN Luxury Tour aims to visit most of them.
Ooh, can I come along too? I can get the Lady Penelope ready at a moment's notice.
I just found out about this from the Frontier's newsletter. Unfortunately I'm working tonight, but I'll refit my Orca and join you on the first waypoint. Time to get that pesky elite on exploring!