If your diagram is correct, the problem may be that you don't have a vent for the sink at all. There should be a loop that goes up from the sink, then tees into the vent pipe.
Vents allow air to follow the waste water; otherwise, the water flowing down the drain creates a vacuum, pulling the water from the trap along with it. In your case, water starts flowing down the pipe in the sink. As it falls, it 'pushes' air out in front of it, up the vent pipe. Once all the water has drained, it sucks air through the sink's trap - you probably don't notice the gurgling from that, since it's following the already gurgling water. Once the 'end' of the water hits the tee, it applies suction to both the sink trap and the tub trap; whichever is shallower will gurgle (in this case, your tub). The toilet doesn't cause problems, because one it acts as its own vent, and two it has the stack vent to draw from.
If water down the sink is causing the tub to gurgle, it's likely that water down the tub will cause the sink to gurgle. Dump water into the tub, and as soon as it drains, plug the tub. If there is no vent, you will hear the sink gurgle as it equalizes the pressure by letting air through.
The difficult fix is to open your wall and install a vent for the sink - and maybe for the tub too, depending on distance.
The easy fix is to get an under-sink vent; I haven't used them, nor do I know if your building code would allow it, but as long as it's legal, it would be the fastest and simplest option: you won't have to open the walls!