How do I apply pheromone oils with precision when tipping the bottle doesn't drip?

Removing the dropper is not a particularly good idea. You then lose any chance of getting a consistent dose and most likely end up with a massive overdose - which from your description sounds like exactly what you got.

For the A314 dropper and many similarly packaged oil-base products including, from what I remember, the company producing your oils - the following helps:

Edited from A314 forum:

Another option is to go to a pharmacy and get a good quality medicinal dropper - one that gives a consistent drop size and use that instead. Even the little thin-pointed dropper that comes with Alter Ego is pretty good if you can get hold of an empty bottle of that.

And if you have not read it yet, the sweet spot post on this thread tells you exactly how to find your effective dose with any product.