I fly a ton with my bike so have a fair bit of experience. With AA they will almost always charge the $150 fee, they rarely miss the opportunity even when you have a smaller soft pack type bag that looks more like normal luggage. The reality is that even a fully disassembled adult bike is impossible to fit within the linear dimensions of the standard luggage size so you are technically over the size limit and that is why they will collect the $150. I've been charged $150 by AA whether domestic or international.
Side note: Like BA, Alaska Airlines is also free for a bike (counts as 1 piece of luggage), it's a good thing to keep in the back of your head as you travel. I bring my mountain bike on most vacations as $300 per trip would add up pretty fast. I tend to use AS for any trip where I would bring the bike for that benefit.