Barring a known injury that prevents you from using the barbell for pressing movements, if you have a problem pressing with your hands at a fixed distance, then you should work on your shoulder flexibility and thoracic mobility. Don’t use dumbbells as a clutch for sub-par flexibility.
I say this without any knowledge whatsoever about you. You might have an injury or something (that you might not even be aware of). And in that case, then it would make sense to use the dumbbells instead of the barbells.
But barring that, work on your flexibility. I could understand if you were trying to overhead press behind the neck, but for the bench press, either you are extremely inflexible, you are using poor form, or you really, really have messed up shoulders.
But that’s all conjecture since, without a video or pics, it’s impossible to know what afflicts you.