Granted, I haven't tried this in a long time, but the first time I did try it, nothing happened.
I made my Runabout my Active Ship and clicked Visit Bridge.
Surely it wouldn't be too hard to make a Runabout interior?
I mean, they're not a very big ship, basically, just a small command module, a bridging section and the cargo hold towards the rear of the ship (a Runabout is basically a flying cargo module, the cargo hold comprises most of the the ship).
And they should make a Delta Flyer interior when that ship comes out as well.
It's somewhat larger then a Runabout, but it's still a relatively small space compared to the larger vessels.