The bad news is that the problem could be much worse than you suspect. In a typical bathroom install, especially if it is greenboard drywall instead of cement backer board, for a tile to be lose may mean that the substrate is degraded. In other words your drywall may be rotting away beneath your tiles. You could try to reset them using a thinset mortar, available at any building supply place. If there is mush beneath your tiles then you might consider ripping out all your tile and drywall and re-doing it or doing a fiberglass surround. You should remove the loose tile(s) and tell us exactly what you find. If it is a hard cement board then you are in luck. If it is soft, mushy drywall then you may be shidada... As for re-grouting, do you have a million little tiles or larger ones? What is the condition of the grout? Does the tile wall flex anywhere when you push against it, especially in the areas with loose tiles or damaged grout? I'll leave grout details either to others or until after you tell us the answers to my questions.