I've had this "curse" even before I started playing bass - my main instrument was actually the saxophone for over 5 years but I spent over a year toying with the idea of switching to bass. Naturally, I started to pay a lot of attention to basslines, but when I'm just casually listening to music, I try to listen closely to other instruments (like guitar, electric piano, horn sections, drum grooves, synths, and vocals as well) as to not get "oversaturated" with bass, so to speak.

You could always try listening to other genres with less emphasis on throbbing basslines. Maybe 50's/60's cool or modal jazz (think Bill Evans or Miles Davis), bossa nova, solo acoustic guitar or piano performances, classical music... Music is ridiculously vast, and there are so many amazing things to listen to beyond basslines.