Considering that Billy doesn't look all that surprised or offended at Frodo startling like that, either he's used to getting this reaction or is just really good at hiding his own feelings about it.

He doesn't even comment on it as he steps closer now Frodo is fully aware of his presence.

"We should go together," he suggests, though his tone isn't forceful. It seems to suggest he'd back off if Frodo was heavily opposed to the idea. "It is safer than going alone."

And hey - maybe Frodo knows more about where to find wintergreens than Billy himself does. He has many skills, but he sure isn't a natural survivalist.