Just for clarity,
bismillah is the actual phrase, while
basmallah is the noun denoting the act of saying the phrase.
@lolfacesayshi: That's actually spot-on.
@Judy: Spelling is fine, as is the meaning. The
literal one is just "In the name of Allah", but the intended use in many if not all contexts is more or less as you said, "May Allah assist me."