There is no hard-and-fast distinction between microcontroller and microprocessor; eg,
http://www.8052.com/forum/read.phtml?id=17429&top=

However, the meanings of "Bits" and "Lines" certainly have nothing to do with it!

In general, I think the term "Lines" is used for physical interconnections - PCB traces, wires, etc;

"Bit" is a general term not even restricted to electronics; it is generally accepted to be a contraction of "Binary digit"
It can be taken in the purely mathematical sense - meaning one of the digits of a binary number, taking the values '0' or '1'
Or it can be taken in an electronic sense meaning any signal (usually part of a larger group of signals) which can take one of two distinct values; eg, ON or OFF; High or Low; etc, etc
It has nothing to do with whether the signal is synchronous (clocked) or not!