If you want as many opportunities as possible with as many different animals as possible, drive. Drive a LOT. Network and find out from the other photographers what animals are hanging out where and when and be there as often as possible. Get up at least an hour before dawn (preferably more) and get to where you want to be before sunrise. Take off around 10:30 or 11 and go nap/eat lunch/relax or maybe go hike a trail if you feel like it. Then by about 3PM or so, get back on the road and get to your target area.
My philosophy is to get a read on what's going on where then stick to one area of the park for a day. For instance, if a black bear sow with cubs is in Tower and that's what I want to do, I will spend the whole day cruising the Tower area, or perhaps the morning in Tower and then the afternoon in Little America.
If you don't have a read on where things are, drive. Go from Cooke City to Lake in a day if you have to, to get a read on what is hanging out where. Then, if the Canyon Pack is crossing at the junction every morning, you know to be there. Or if the Mollies are near the road in the early morning at Little America, you know to be there.
As a rule, you can find grizzlies more often in the Dunraven area in summer as they like to go high when it gets hot.