do native speakers use 해수욕장? in my experience from watching dramas and reality shows, they just say 바다
해수욕장 is commonly used when naming a distinct beach. For example 해운대 해수욕장.
While I don't know if native speakers use one more than the other, I found that 해수욕장 is (this is taken from translating it from the korean dictionary to english via google translate) "A beach with a good environment and facilities for bathing." While 바다 is (again, translated from the dictionary via google) "Woven water covering an area close to three-quarters of the Earth's surface. It is largely divided into ocean and annex sea, and its annexes are divided into Mediterranean Sea and coastal sea." (Doesn't make much sense, but in layman's terms: A sea/ocean.