One big thing- Take your leather out into the sun. It opens the pores and allows the oil to soak in.
If you try to oil leather dry and in the "dark", it really doesn't soak in as deep, and just hits the very top part of the leather. Another reason why leather feels slimy and oily sometimes.
Focus on the back part of the leather (the side that touches the horse). The side you see, has been coated and treated to look all pretty and shiny, and doesn't accept oil as readily. The back side isn't, and it's the porous side that soaks in everything.
I give mine a good clean and condition- let that dry. Take it completely apart, and set the pieces somewhere out in the sun for a little while. Once it feels kind of hot, get a sponge drenched in oil and start coating the leather. Work your leather.
If you oil and oil and oil, it helps, but you really have to roll it around, gently bend it, etc while your oiling. Wipe all the pieces off lightly, then stick it back in the sun and keep checking on it. You'll need to periodically wipe it down until it's totally dry (this can take all day depending on the weather situation). Just keep repeating this until it's where you want it.
It's a long process, but once you do it, your leather is fine with just periodic conditioning, and remains pretty soft. Some people feel using a ton of oil leaves it slimy and greasy, but it's why you set it in the sun where it soaks up everything, and keep it wiped down, and wait for it to completely dry. Then wipe it down some more. You really have to be careful though, and determine your leather quality. High end bridles, really are fine with just a good conditioning. Others not to high quality, will need a big oil drench. Take it fairly slow, and remember-Your leather will dry. Just keep going until it's how you want it. It'll be a oily mess when you're doing this, so fair warning.
And remember, with use it will form to his head and break in even further.