Not sure about the bug but the flower looks like some kind of hibiscus :) The flower may even be a marsh mallow. Was it growing near water? It looks like the marsh mallow I see at the beach too which I think is in the same family as hibiscus.
I would say this is a Hibiscus. I have 4 hibiscus plants in my yard and one of them produces flowers exactly this color (white with red center). The others are red, pink, and yellow/red. The center stem is different from the Rose of Sharon flower (as you stated above). I have those growing in my yard too.
Do you recall what the plant itself looked like? The Rose of Sharon can get very tall and grows as a large bush. The hibiscus has several long stalks coming up and grows to about 4 to 5 feet in height. The hibiscus stalks die off each year and regrows new stalks. The Rose of Sharon continues to grow from the prior year's stalks and can form an extremely large bush.
It's a hibiscus, but some flowers in this family are called "Rose of Sharon" or "Mallow" so I would consider them possible synonyms. Don't forget blossom, bloom, floral, flora, pistil, stamen, petal, horticulture, horticultural, and so on.
This is probably information overkill but I am a bit of a plant geek at times.
From the USDA.gov site - probably more info than you would ever want on that site, but there seems to be some confusion on the plants. Sorry the link would not paste in correctly.
Hibiscus syriacus L.
Click on a scientific name below to expand it in the PLANTS Classification Report.
Kingdom Plantae – Plants
Subkingdom Tracheobionta – Vascular plants
Superdivision Spermatophyta – Seed plants
Division Magnoliophyta – Flowering plants
Class Magnoliopsida – Dicotyledons
Family Malvaceae – Mallow family
Genus Hibiscus L. – rosemallow
Species Hibiscus syriacus L. – rose of Sharon
Then beyond that add on all the varietes/cultivars that are being developed and sold by the nursery industry. They can all look very different and have extremely different characteristics but are of the same species.
I was not saying it is a rose of sharon, I was just saying that rose of sharon is a hibiscus. I just thought it would help if people saw the "family tree". Someone at some point indicated they were two different plants, as in the rose of sharon was not a hibiscus (maybe I read it wrong). That is all I was getting at. :)
@ Murray were these in the wild or in a manicured landscape? If in the wild and near the bay it is most likely the Marsh Mallow variety. I love these flowers they are so beautiful! I can't wait to try out my macro on them the next time we head to the beach :)