A sharp 3 or 4 TPI blade is the best first thing to try. A slower feed rate can also help, but if your blade rubs against the wood fast enough and long enough to produce significant friction, too slow a feed rate can cause burning.
If you've bought a bunch of high TPI blades after discovering that a higher tooth count often produces a cleaner cut, you may be wondering why a low TPI blades even exist.
Why is it that a slower feed rate and low TPI blade can eliminate blade drift? The simple explanation in many instances of blade drift, burning, and binding with any type of saw is that the blade has nowhere to go.
You may have noticed that a blade with a high tooth count consequentially also has smaller, shallower gullets; and a blade with a low tooth count can have very large, deep gullets.
Gullets are more critical to a blade's function than most people realize. Once you cut the wood, you need to get it out of the way so you can take your next slice. If the blade's teeth slice off material faster than the gullets can carry the material away, that material compresses to the point that it can't compress any more, then it starts pushing back on the blade. At this point, the blade follows the path of least resistance, which often means drifting to one side or the other, where the material is less compacted and cannot provide as much directly opposing force against the blade's forward motion. As you cut thicker material, you need deeper gullets to carry away the waste.
Mattias Wandel has an excellent visual explanation and accompanying video titled, The Physics of Bandsaw Resawing, but the same principles apply to any blade.
If you still have problems with blade drift after trying a sharp 3-4 TPI blade, there is a great video by Alex Snodgrass demonstrating how to properly set up your bandsaw and guides.