Thermal bottoms are the best choice. They can be had in different weights for different degrees of warmth. If your bibs are insulated, a lighter weight may be the best choice in the mild temps we have around here. If you are going to Vermont in January, you will want heavy weight. If you just want to go the Sears/K-mart/etc. route, avoid the waffle pattern ones - can lead to chafe-a-rama. Ditto for just wearing regular underwear under the bibs - they are not neccesarily made to ride directly against the skin.
With most thermal bottoms, getting too hot is only an issue when the temps are above 35 F.
If it is frigid, I'll wear thermal underwear underneath the sweat pants instead of regular underwear. I bought REI-branded thermal underwear (I believe it's expedition weight; they come in various thicknesses) and it keeps me toasty.
Where I've had problems is hands and feet - they always get too cold. I finally bought a nice pair of Marmot gloves - they were expensive but well worth it. And I discovered that it's better to wear one pair of socks instead of two - that, and a good pair of boots, helps keep the feet warm. (Of course, we all know that keeping the head warm keeps the rest of the body warm!)
The most effective tip I can give for avoiding cold feet is to unbuckle the lower two buckles of your ski boot when in the lift line and riding up the lift. Wiggle your toes and the natural blood flow will warm your feet up. I actually spend a lot of time skiing with the lower two buckles undone, which gives you a much better feel for the snow.
Hope this helps.
If you must wear a natural fiber, try and use wool as it is warm even when wet.
I skied all day Sat. with just my Thermaxs, bibs and coat. Temp was about 38 and calm.