How to zero in on the mot juste?

English has very, very few "true synonyms" - by and large, each similar word (or phrase) carries an individual nuance.

Whereas I agree with Michael Harvey that there are no shortcuts, I suggest the OED, which gives examples in context.

Here, the important point is to note the differences - not the similarities

Bevy:

2. transferred. A company of any kind; rarely, a collection of objects.

Group:

1. A number of things placed together as the result of deliberate arrangement or composition.

2 b. A number of people or animals standing, positioned, or located close together so as to form a collective unity.

The OED also give etymologies and, at the risk of the etymological fallacy, it is always worthwhile considering a word's original associations.

Bevy is not a good example, as its etymology is unclear, but it seems to be associated with pleasure and is thus positive.

Group originates in a military detachment and is therefore neutral.

A caveat is that the OED is not, as yet, fully updated and a lot of modern usage is excluded.

Then there is Google Ngram Viewer which will give frequency results that can usually be checked in context, but this is restricted to published works.

Google Ngram Viewer Search term a bevy of * and then 'a group of *' (and thereafter checking a representative number of examples in BE and AE.

Then there is the British National Corpus and American Corpus.

And then there is the "Online Collocation Dictionary" https://www.freecollocation.com/

I imagine that combining all the above and your current knowledge will probably reduce the error rate in your decisions to about 2%.