The AISC Steel Design Guide 1 doesn't have an example for biaxial bending. Perhaps you could analyze it about each axis then combine the forces to determine the thickness.
Try the AISC website; they should be able to offer an opinion.
newbie,
The simple answer is:
(Mx)/(Sx) + (My)/(Sy) <= 0.75Fy (AISC 9th ed.)
You really need a Senior Engineer's guidance on this. It's not just a simple calculation. You need a good grasp on section modulii of bolts and plates.
I'll try to answer:
The biaxial bending is going to send a portion of the area under the plate into tension, which, BTW, it can't take. So this tension is transfered to your anchor bolts. If you have 4 bolts, you might get lucky and only have the corner one in tension. These anchor bolt tension loads are now point loads on your plate. The rest of your force couples are going into compression on your pier/footing. Find your maximum moments and apply the above formula. As I said, it can get pretty nasty.
An acquaintance has written a spreadsheet for uniaxial bending of the base plate. It's only for bending about the strong axis of the column, but, if you can find the maximum tension you have in your bolt under your loading condition, you should be able to back into an answer (increase your moment until it matches your calculated tension). Find the minimum width of base plate at your resultant's location, and use it as your plate width. I haven't gone through the numbers, but it should work. Make sure you have a senior engineer look over it. You will still have to go through the biaxial calculation for pressure on the pier to make sure you don't exceed allowable.
You want "baseplt9" from his website. Make sure you thank him for it.
You'll have to cut and paste in your browser
In reality, there is no straight forward solution to this situation.
Practically, follow the suggestion by bridgebuster - analyze one axis a time, and add results from both directions. By doing so, you can get approximate area under compression, and tension that is to be taken by anchor bolt(s) outside the area.
Do hand-cal a few times before jump into spreadsheet, you will gain better feeling on the whole process
