Asteroids with Volcanic activity
According to research by Professor Lionel Wilson as described in this articlethis article, there are asteroids with volcanic activity that much resembles the volcanic activity on earth. This means that your asteroid base could use geothermal energy as the only necessary source of power. This base could also be located by a volcanic hot spot on the asteroids surface in order to further disguise any escaping heat from your base. I am not quite sure exactly how common there asteroids are, and if they are rare or valuable enough to be significant sources of interest.
In addition, it may be that bodies with sufficiently large metal cores could, through a [geodynamo][3]geodynamo, generate a protective magnetic field, assisting in disguising any escaping signals and protecting your base from high energy particles, solar wind, etc.
As for your requirements:
Size of the asteroid - I assume that any asteroid large enough to have volcanic activity would also be large enough to serve as a base. Any concern would likely lie in the other direction, with concerns over size and conspicuousness.
Composition of the asteroid - This asteroid would likely have plenty of resources, as it is larger and has sufficient metallic content to form a metallic, molten core. Again, concerns would be with standing out and being too attractive. However, in a civilization with a galactic economy, it would likely be an extremely long time before an attempt was made to exploit an asteroid that is far enough off the beaten path.
Power source - Solved above. Would definitely require a certain level of sophistication in technology and heavy equipment.
Propulsion - In a civilization with the ability to travel through space, there would almost certainly have to be very detailed maps, including current and future location, velocity, and direction. Any significant change in predicted pathing would likely be discovered extremely quickly, unless the asteroid is in a location that is rarely "scanned" or hidden. Again, if you pursue a scenario where the asteroid is extremely small and far away from inhabited and traveled locations, you could get away with it.
"Gravity" - Asteroids large enough to have volcanic activity are not necessarily large enough to have sufficient gravity to live comfortably. 4 Vesta, the asteroid named in the aforementioned article, only has a gravity of 0.025g, or 2.5% of earth's gravity. I would approach solving this by having the base located below the surface of the asteroid, with a spinning living space or large spinning space with the axis anchored to the asteroid's rock.
Proximity to other heavenly bodies - As these asteroids are fairly noteworthy, one would likely have to chose a one orbiting a star far away from population centers, depending on the proclivities of the civilization with relation to mining and exploring asteroids. An asteroid floating in the cold of space would likely radiate heat until it cools, but that process would likely take millions of years.