Although there are many products offered for use as chaulks suitable for use in the shower/tub area, most of the "long lasting" products have a silicon base and are generally "guaranteed" for a specific period of time. Regardless of the product used, if you are having trouble with the chaulk material adhering, make certain that you have thouroughly cleaned the tile and tub surfaces before applying the chaulk. I will generally use acetone as a solvent before applying a chaulk. A small amount of expanding foam insulating material makes a good filler. After injecting it into the crack and allowing it to expand, it may be trimmed appropriatly and chaulked over. Good luck.

Just one small piece of advice. Don't use "adhesive" caulk. If you ever want to remove and replace it, you'll have a job trying to remove it.