Meaning – What Does ‘Save (One) the Trip’ Mean?

"Save the day" is an idiom. It doesn't mean to take advantage of the day. If somebody saves the day, he does something to successfully prevent a likely defeat, failure, or unpleasant situation. For examples:

We are expected to lose the game, but our tailenders (lower order batsmen) played well and saved the day.

The police saved the day by coming just in the nick of time and catching the kidnappers.

We forgot to bring a knife for cutting the wedding cake, but Peter brought one and saved the day.

"One too many" is a shorter version of "[have] one too many", which generally means having had too many of something, not necessarily only one too many, but any number, so roughly, it's "too many" or "too often".

By far, the most common use of this phrase is about the amount of alcohol someone has consumed, and if the context doesn't indicate what there's too many of, it's understood to mean too many alcoholic beverages, which is the case here.

So in this context, it means:

She has drunk too much alcohol.