It might work.
A 9x13 pan means the dough is never too thick, and the heat reaches it rather evenly across the sheet.
A bundt pan is very tall YET there is that open space in the middle, allowing the heat to reach the ring evenly. Still, it is a bit thicker across the cake section, than you get with a sheet cake.
I have never tried what you are asking. And I don't like to change the parameters of a recipe unless I don't CARE if it turns out or not. I am happy to experiment is the cake can be thrown away without remorse if it doesn't work out.
I would be tempted to reduce the oven temp a bit and increase the cooking time.
BUT I think the BIGGEST problem will be getting the cake OUT of the bundt pan.
Bundt cake recipes are very firm cakes, and with proper pan preparation, the cakes WILL come out of the pan whole and intact. If you are making a regular type of cake (either from scratch or from a cake mix), it is quite possible your cake will fall apart when you try to remove the baked cake from the bundt pan.