: as Tom says, the buses are modern and comfortable. You will be pleasantly surprised.
Airport to the Otogar
: take the Metro. Here's a map showin how many stops you'll have to take: http://www.turkeytravelplanner.com/Maps ... o_map.html
It's a short walk from Arrivals to the actual Metro - it's part of the airport and it's clearly signed.
How much of an event is it going to be to get on a bus and travel to Bursa?
: apart from the jet lag, it's not going to be a big drama. The most challenging bit will be navigating around the otogar because it is big and can be confuing. Don't be put off but sales persons approaching you - they're usually very helpful. Tom lists here http://www.turkeytravelplanner.com/Wher ... table.html
the ticket offices at the otogar. I can recommend Nilufer for the ride to Bursa - peron 105 -106. They (like alot of the companies) even have an e-ticket facility on the website if your Turkish is up to it! Even if it isn't you'll be able to check out the departure times (and likewise for the other companies that go to Bursa).
: no worries. You'd be amazed what goes underneath and the attendants will be quite helpful. They'll probably give you a ticket for each bag so that bag and owner can be matched on arrival. Make sure you have a book or whatever in a small "carry on" sized bag.
Is there anything I need to be aware of?
No, not really. If you're a man they might try to ensure that your seated next to another man and not with a single woman. Umm... that's about it. The food and drink on the bus are free. I had a nice ice cream last time with Nilufer: yum. When you arrive at Bursa are people picking you up? If not you'll need to catch a bus or a taxi into town itself because the otogar is a little way out.