I took a recipe that a called for 45 minutes at 350 in a 2" tall 9" pan, doubled the recipe and put it in a 4" x 9" tub pan.
Are their any rules of thumb to use when converting a recipe over to a tube pan for cooking time?
This Answer: https://cooking.stackexchange.com/a/42163/6440 explains general pan size conversions, but a bundt or tube pan is not the same thing.
This article in the Serious Eats is pretty comprehensive about conversions and guesstimating baking times, but there is no precise mathematical formula, you'll still need to keep a close eye on your cake to define the final time
General rule of thumb in the article states that cakes in tube or Bundt pans require roughly 1 minute per ounce of batter (slightly faster compared to a simple round cake pan which takes between 1.2-1.29 minutes per ounce, since tube / Bundt pans have a higher surface to volume ratio than simple round pans)
A 9" pan filled up to 2", according to a table in the article, has 28 ounces of batter. Doubling up, that means 56 ounces of batter. Therefore, you should expect your cake to cook for something between 56 to 67 minutes and DO NOT MESS WITH THE TEMPERATURE.
Best approach would be to leave the cake baking for about 50-55 minutes and then keep an eye on it every 5-10 minutes for visual and texture cues before attempting the toothpick check
