I have a little girld that is 4. She has never and will never wear a bikini! She is in a tankini, just because potty is easier. I told my mom that it is getting harder to find them though. I decided if I couldn't find one, then I would rather fight with a one-piece. We NEVER let her go around in just a diaper either. She wore cloth, so trust me, some were OH SO adorable! I still put a dress or skirt on with a normal shirt. She even puts on a white tank under her spaghetti strap tops b/c I have told her to for so long. She will do it without being told now.
She wears bermuda shorts (she's the same height of a 5 1/2 year old). She also wears shorts under all skirts and dresses. (Or leggings) I'm old school. (I'm only 27, so it's hard to be old school with the rest of my generation going nutso.)
All-in-all, you're not being a prude.