Q: Is it normal to feel a `click` on my elbow when bench pressing? I don't feel any pain however.
The click on your elbow could be from your triceps tendon as you bend and straighten them, but this is not normal. You can try and bench press using a lighter weight and see if the clicking is still there. Using a much heavier weight may eventually lead to inflammation of your triceps tendon, so do adjust and try to find the right weight for you where there is no clicking.
Another thing, here is an article by Rick about 5 ways to make the bench press more friendly: https://exercisesforinjuries.com/5-ways-to-make-the-bench-press-more-elbow-friendly/