(C) is definitely out. When a negative or limiting adverb is moved to the front of the clause, then there must be inversion of operator (first auxiliary) and subject. (c) has the normal S - aux
vb order and is therefore grammatically incorrect.
Of the other two, (b) is the most obvious and undoubtedly the one that would be marked correct. The verb indicates that this is a suggestion and therefore the most obvious context would be that the person is making some sort of recommendation for future action :
I think you should go / Why don't you go, and when you get there (blah blah) This would be reported as in (b)
It's not completely impossible though that she is suggesting that something might have happened in the past :
I think he probably went, and when he got there (blah blah)
This would be most likely to be reported as :
She suggested not only that he might have gone but also that when he got there (blah blah)... - or, if you want to retain the inversion
She suggested that not only might he have gone but also that when he got there (blah blah)... However, (a) is not impossible and it's certainly not grammatically incorrect. Both (c) and (a), incidentally, sound much more likely with the inclusion of
that. The fronting of the negative adverb gives a slightly more formal feel to the style, and the inclusion of
that would be in line with that type of style. Omitting it, for me anyway, creates a slight stylistic tension - the style is no longer coherent.