I think this is one of the things that just continually improves as long as you keep playing (well, granted that you don't restrict yourself just to the signatures you're already familiar with). I remember I struggled a lot with time signatures other than 4/4 when I had played the guitar for, well, a lot less than I have played now.
Are you playing with a track or metronome or just by yourself? I find it's easier to get the time in my head if I listen to the song played by a band with a drummer. The drums really help me with getting the beat right. If I just have a score (or tablature), I try to "hear" how the drums or a rhythmic bass line or piano accompaniment (depending what's appropriate within the context) would sound, then just play along. I never liked tapping my foot, I found it much easier just to slightly nod on the emphasis. (I suppose this is "dancing inside".)
I remember I used this with the guitar for learning how to improvise in odd time signatures:
http://www.youtube.com/watch?feature=player_detailpage&v=Z9IQnDRYIYU#t=547s (the end section of Starless by King Crimson). I've recently jammed along the same track with my tenor, although the original wind instruments on the track (IIRC) were alto sax and cornet. The time is 13/8, 4 bars in Cm (concert pitch), 2 in Fm, then 2 more in Cm. Then it shifts to 4/4 Gm for 4 bars, then goes back to the 13/8 thing before going back to the song's main theme. It's very easy to play along with the sax as it's mostly in C minor. I actually count the time as 1-2-3-4-5-6-7-8-1-2-1-2-3, because that's how the drums and bass sound like to me.
Anyway, have faith, as I think this is something that will just come along, but is difficult to rush.
Cheers,
Jori