I’ve done this before many times and never realized it may be problematic, If eggs or baked beans are placed in a non-kosher bowl and subsequently poured onto a hot pan, will the smell of the cooking eggs or beans extract taste from the treif bowl?
I don’t see any issue with this. The eggs at the time that they were in the bowl were cold, and an empty hot frying pan does not give off zeiah (steam) or reicha (smell), therefore your eggs are still kosher. In general, it isn’t a good idea to use non-kosher utensils for food, for a number of reasons. The first one being is that things can get mixed up or something hot added to it. Therefore, for the future try to use a kosher bowl.