Learn English – Why use the word “chasm” instead of just “gap” or “hole”

And answer came there: None.¹

You could possibly replace "the previous experience I had with them" with prior experience. Although it's slightly ambiguous, the context and the use of prior would imply "with them".

I've chosen them based on prior experience.

I don't think there's a way to express "prior experience" in one word and retain the "with them" aspect.

¹ after Lewis Carroll (misquoted!)

She reduced the gap between the dates of taking tests. She used to take it one month and the other, now she takes it after every 15 days.

If this has become a regular occurrence, the OP could simply shorten the sentence above to

She now takes tests/sits exams every two weeks (OR) every fifteen days
She (now) sits tests once a fortnight.

For an alternative way to express: "to reduce the gap between two dates" I would suggest interval and shorten

She has shortened the interval between her tests. She used to take them once a month but now it's every 15 days

Merriam-Webster defines shorten and interval

shorten
1. to reduce the length or duration of

interval
1. a space of time between events or states