Please reset your expectations: grab 10 bullets out of the box. Measure them base to tip. Write down the answers. You will probably get a range of at least 0.005, perhaps more. Quality bullets will have a smaller range than cheap ones. Until you start pushing 100-yard group sizes below about 0.4, bullet length by itself isn't particularly important.
As pointed out elsewhere, the seater doesn't push on the tip of the bullet, it pushes on the ogive. High-quality bullets have a more consistent shape so you get more consistent seating depth. When doing quality control on your loaded rounds, check against the ogive.
RCBS makes precision mikes, I really like mine and use them every day to check post-sizing base-to-datum.
Brass neck tension affects seating depth and thus COL. The solutions to that problem include annealing and a neck expanding mandrel or that nifty (and expensive) K&M seating force press.
I haven't heard of anyone doing this lately but if you polish your bullets in a vibrating tumbler, there will be more size variation.
Make sure that the die is tight in the press (tight, not gorilla tight) and the seating stem is locked down. When sizing, I use lock rings with flats like a nut and torque the die onto the press. I use 70 in-lbs, that is INCH-pounds, not foot-pounds. That isn't much torque but if I anneal first and lube consistently, I get very consistent case lengths. I use a Girard case trimmer and since I have consistent headspace I also get consistent case length. Since I annealed and expanded the necks using graphite and an expanding mandrel, I get consistent neck tension and consistent COL. As you are working with your components watch for odd things. For example, when sizing if you have a case that takes more or less effort than normal set it aside. When seating bullets, same thing - set aside the easy and hard ones. Tolerance-stacking is your enemy.
Don't flip out because the base-to-tip COL wanders around a few thou.