Cougar are very hard to find. They end up finding you on accident. Ran into one when I was like 12 in California (Ok, ran AWAY from not into ha!), one when fishing in 2004/05, i heard two last year right nearby but there's a chance they were Bobcats, and one this year that didn't do so well. If you don't have dogs (which are illegal) to chase them down with, then you have to count on bad luck to bring one to you.

I can probably put you into a Bear if we both have a good week to camp out in a few canyons on the Peninsula and in Skagit area. When I go on a hardcore Bear hunting outing, I like to hunt in teams. Usually three teams of 1-2 guys. Surround a big area and work inwards since Bear will spook easy and if they run away and you lose them, they will be heading toward one of the other teams.
Also, you can do the online course but it is only the written portion. You still need to have an instructor sign off that you have done the IN PERSON field safety course.