Hi Carol,
I am not sure about the USA connection, there seem to have been Ainslies in Kentucky for years. I searched Shipping records and Ellis Island records, but no results. According to one in the 1850 census, he had married and had 2 children, so he must have been in America since 1846/47 at least. I can see a marriage on 19 Nov 1844 for a George Ainslie to Mary Thirwell in Jefferson County, Kentucky.
Maybe you have other proof, that I have not come across yet.
Tom