"Sunbathe" to czasownik sam w sobie. Będzie się zachowywał podobnie, jak np. swim:
Present Simple:
I often swim in the summer. I often sunbathe in the summer.
Present Continuous:
I am swimming now. I am sunbathing now.
Past Simple:
I swam a lot last summer. I sunbathed a lot last summer.
Past Continuous:
I was sunbathing and my children were swimming, when suddenly the sky got dark.
Present Perfect:
I haven't swum in an ocean before. I have already sunbathed three times this month.
Future Simple:
I will swim. I will sunbathe.

Inne użycia, np.
po czasownikach modalnych:
I love summer. I could swim all day. I could sunbathe all day.
w formie gerund:
I enjoy swimming. I enjoy sunbathing.
w konstrukcji "used to do":
When I was young, I used to swim a lot, but I didn't use to sunbathe so much.