Is it possible to use burst mode with self timer on Nikon D3100?

If it's not possible can anybody recommend any good cameras that are able to do this or have very good shutter speed?

With my Nikon D90, in the Custom Setting Menu (pencil icon), Timers/AE lock, Self timer there's a setting for the Self-timer delay (choice of 2, 5, 10, or 20 seconds), and a setting for Number of shots (1-9). I think that number of shots is the self-timer with burst mode setting that you are looking for. If that is absent in the D3100 you may want to look at a store sample of D5100 or D7000.

NO. No camera can do that

You will need to use a remote shutter release

Nikon sells one for your D3100 for under $15

Not with a dslr. To use burst you have to press and hold the shutter release. As soon as you let up the camera stops shooting.