How can I resuspend a cell pellet without harming the bacteria?
Assuming that you are talking about E. coli: As long as you are resuspending the cells in a suitable liquid, e.g. fresh medium or buffer, then from my experience you don't have much to worry about - the cells are very robust. I've found that different strains and growth conditions give pellets with very different qualities - some will resuspend quite well with vortexing. If the pellet seems clumpy then trituration is something that I always found to work - pipette up and down until the pellet breaks up.

If you were going to do some kind of physiological measurement with the resuspended cells then it might require some checking, but if you only intend to regrow and induce expression I would say that giving the cells some time to recover in the new medium (check that absorbance is increasing) before inducing expression should be enough.