This is one job that drives me crazy. I tried everything-I filled the tub with ater, ran the bead around the tud, and (tried) to even it off with a scraper. The results? Uneven caulk, and messy cleanup.
How does one do this properly?
Use a bead-forming tool.
What is the point of filling the tud with ater?
A plastic spoon will do the job too. I find that pushing the tube forward (towards the opening) instead of away from it gives better results - it forces the caulk into the crack and the tube opening helps to smooth the bead automatically.
My friend (who is much handier than I am) had a beer mug full of dishwashing liquid in his bathroom while installing it. I asked him what it was for, and he said he would put the caulking on, then dip some soap and just smooth the bead down by hand. It all ended up looking quite nice FWIW.
A finger dipped in water for smoothing works too.
Smooth and steady is what it’s all about. I used to manage an apartment complex and the other managers very quickly learned to assign me all of the caulking jobs. I can get a perfect bead virtually every time, and it’s apparently not something that can be taught. (Either that, or the other managers were smart than I am).
I do best with a tube that you squeeze by hand (as opposed to one of the “caulk guns”). Cut the tip of the tube a little bit more narrow than you think you need, and at an angle.
First, clean the tub and get any old caulk off.
Second, dry the surface. If there’s any noticeable moisture (even in the crack where you can’t see it), the caulk won’t stick well. Often, I’ll clean the tub and come back the next day to apply caulk. (OP, my guess is you had WAY too much water around).
Third, apply the caulk. You have to keep the pressure on the tube, the speed of your hand and the distance from the tub enclosure as constant as possible. You cut the caulk tip at an angle, so use the longer part of the tip to automatically smooth the caulk into that perfect concave shape as you apply it. If you have to adjust your grip, “cut” the stream of caulk with the angled tip and release a little pressure on the tube so that it sucks the caulk on the tip back in. Then adjust your grip and move it back to the same distance from the tub/wall to continue.
Fourth, you can do some touch ups, but you shouldn’t have to if you did the third step right. A damp (not wet) finger work well to smooth out patches. Use each finger once, then go wash your hands in the sink and partly dry them on a towel before doing more smoothing. For smears on the wall or tub enclosure, use a damp paper towel or sponge.
Fifth, bask in the accomplishment of a challenging task that provides you with absolutely no importance or recognition whatsoever. 
The usual DIY fault is to use about 2x too much caulk. It has to be dispensed evenly with no gaps. If you’re thinking of the smoothing with a finger or tool as a process to move caulk from the too-full areas to the too-dry areas, you’re Doing It Wrong http://www.doingitwrong.com/ .