Had a quick go with some success as you can see from the screenie below.
I used wine 1.12, not the 1.01 that comes with Jaunty (from the archived debs off the main wine page) - after seeing the comments from the guy who got it to work. I switched Wine to Win98 and emulated a virtual desktop (1024x800). Installed BZ and BZ 1.4 patch and deleted the anims folder...and then started it by the command line (i.e. wine bzone.exe). I used hardware acceleration.
Two problems so far:
(a) When playing there is a loud sound in the background that seems to correspond when the tank is on the ground (kinda) - changing audio settings in game doesn't help
(b) I'm getting "err:d3d7:IDirect3DDeviceImpl_3_GetRenderState Unexpected texture stage state setup, returning D3DTBLEND_MODULATE - likely erroneous" a trillion times a second
Haven't tried MP or TRO. Video works fine.

Edit:
Tried MP and played a game of stock colli with Westpac..apart from my severe lack of skill there were no problems..aside from my FPS being way high (100+) - I know this can cause problems - is there a fix? Inputting my name into the MP pre-lobby screen was a bit 'sticky'. Westpac reported no problems from his side
Music doesn't work..despite me using an original CD - it obviously detects the CD from the fact that I can play SP missions. Hmm
Another screenie:

Edit 2:
On the most current Wine version and using Jaunty the problems are (so far):
(a) Sound is lagged by a fraction of a second - this is a pulseaudio problem. Going back to ESound solves it.
(b) The 'pointer' in the game is missing - you know when you are going to put down a building or show a unit where to go..well the line between the square and the HUD has gone.
(c) The background sound fx are kinda messed up (not the shooting or voices or anything) but it sounds like the background noise is turned too far up (kinda difficult to explain). Going to keep on looking - pretty sure this is a straight wine problem =/
(d) I can't seem to reliably get it to work fullscreen - sometimes it crashes X, sometimes it leaves me with a BZ resolution desktop..sometimes it works...and the screens don't auto-stretch, so the mission selection / load screens are in a 640x window, then it goes to a 1024x windows (i.e. the size window I want) for the game. Not a huge problem