Do I need to do some drying before filling a small gap in the bathroom caulking?
OK, you had me at "a bulge with cracking". This is a little scary. Even though you don't feel any moisture doesn't mean it's not pooling on the top and rotting the wood. Tubs are heavy and tubs filled with water are a lot heavier. I really think you need to check into this a whole lot more unless you want a tub in the basement. You mentioned LVT flooring in the bath. You might want to consider removing a few planks and examine the subfloor. Hopefully some planks were leftover from when the floor was put down. If you determine all is good, a good silicone caulk applied after everything is dry and scraped clean is all you need. As mentioned above, try to eliminate the water running down the side or at least throw a towel down there before showering. Good luck.