do I need to adjust the cooking time for a pound cake baked in two separate bundt pans instead of one regular tube pan?
If I understand your question, each cake has 1/2 of the batter. If that's the case, each cake is smaller, so it will bake faster. You will need to reduce the baking time, but it's difficult to tell by how much, especially without knowing how deep the layer of batter is in your pans compared to the one used by the author of the recipe. Usually the bake time for half a cake will be more than half the original bake time. My guess is your final bake time will be between 45 minutes and 1 hour. The way to approach this is to bake for about half the bake time, then check on the cake occasionally until it's done. Your initial checks will be infrequent, but increase the frequency as the cake gets closer to done.
I would bake for 30 minutes, then sneak a peek and see how they look. If the cakes still look soft/gooey/liquid in the middle, wait 10 minutes and check on them again. Keep baking until the cakes no longer look raw. Then take one out and stick a cake tester, thin knife or kebab skewer in the middle. Pull the tester out - if it comes out with liquid batter or partially cooked batter (that looks like a thick goo or paste), the cake isn't done yet. Wait 5 minutes and test again. Repeat until the tester comes out &quot;clean&quot; - that is, with no batter on it, but maybe some crumbs and a sheen of oil.
Since bundt pans have ridges that make some sections of the cake thicker than others, try to test in a thick section, because those will be the last to finish cooking.
Tips:

Try not to open the oven any more often than necessary, because you lose a fair amount of heat every time, which will slow down the baking.
When you move the pans, try not to knock them around, because this can knock air out of any liquid portions of the batter, which will make the cake sink in the middle.
With two cakes baking at the same time, they may bake unevenly. The first time you check on them, swap their positions. That will even them out, so they don't get over-done on one side and under-done on the other.
Pound cakes usually develop a crack in the middle of the top - try to sneak the tester in through the crack so the hole it makes is hidden by the crack.