I drink Bulleit all the time, but I was unimpressed with it in the beer. I noticed a difference between it and the Woodford. Not a huge difference, but the Woodford was better.
As for how much to add, that's something you need to figure out for yourself. Take a sample of the beer at a known volume, and add a little bit of bourbon at a time until you get the desired flavor, and then calculate how much to add to the final product.
That's something I'd do after oak aging, before bottling. A little bit of bourbon goes a long way, so don't be surprised if your desired flavor is hit with as little as 1/4c of bourbon. I've used 1/2c before, but it was a bit too much, IMO. Your mileage may vary, etc.
I would also recommend using about 1oz of American oak cubes for 2-3 months, or 1oz of chips for 1-2 weeks. A lot of people argue about whether cubes are better than chips. From my experience, they're both good, but different. I prefer cubes for beers like you're making, but I use chips a lot on different beers. For a big beer that'll be aging for a while, the cubes are a good way to go. I like to use chips for smaller beers that won't benefit from extended aging, like IPAs or regular stouts.
The last bourbon oak beer I made was about 10% ABV, aged it for 2-1/2 months on 1oz of cubes, added bourbon to taste at bottling. It was good after 3 months, and fantastic after about 6 months in the bottle. It started to fade after 9 months. It's a little over a year old now, and it's definitely not as good as it was 6 months ago.
Some people like to add vanilla extract too, but there is a lot of vanilla flavor in the oak and bourbon. I prefer subtle flavors in my beers. I've had too many "vanilla porters" where I drink it and think "wow, they dumped a lot of vanilla extract into this beer." I think the flavors should work together, and consider one overpowering flavor a fault in the beer.