The use of "a bit" in this sentence is rather out of the ordinary but it is nevertheless grammatically correct. It indicates that the person has some information (a story, if you will) and is about to tell a small part of it. I would not say it this way but perhaps, "Let me tell you a little about it" with the understanding that this is not a translation of "Laissez-moi vous raconter un peu" but a more conversational way of expressing the intended idea.
The only times that I've seen inversion is when asking a question and thought that it could only be used with questions. So I guess more explicitly my question is, when can/should one use inversion outside of asking questions?
This may be a really basic question as I've never taken a course in french. Therefore most of my grammar knowledge comes from patterns that I have noticed while completing the lessons on this site and not from formal classes on french grammar.
I think the problem is that the "vous" here has to be taken as an indirect object; there seems to be an understood 'topic of conversation' that's in effect the direct object of "raconter" : "to relate X to you ." The phrase "un peu," "a little (bit)," seems to be the object here: "to tell you a little bit [of it/them, about it/them]." I would have expected our old friend "en" here, except I guess you "raconter" directly (not "about").
"a bit" is an idiomatic way of saying a small quantity of something (even things that are not easily quantifiable like part of a story). The problem with this sentence is that it is most likely a French translation of an English idiom that gets re-translated into English. It was probably originally an English sentence like:
- Allow me to expand on that a bit
- Let me tell you something
- (highly colloquial) I'll tell you what.
Out of context, it is hard to know the meaning of the original sentence.