The third form of emphasis used by Bike is Highlight (⇧⌘H), which uses the standard HTML <mark> tag.
You could paste unindented text, preserving highlights and other formats, into Scrivener using a script like this (originally intended for Apple Mail):
If you are very strongly attached to <u>, which sees less use these days, we might also be able to write you a script which pasted Bike highlights as RTF underlining.