I am trying to figure out the Punjabi names. Can you explain where you got the `virtuous' meaning from? Actually the sikh name site http://allaboutsikhs.com/names/names.htm is remarkably accurate, and suggests something else.
What I thought was that the element jas arose from the sanskrit yashas, a word going all the way back to the Rgveda and meaning beauty, worth, graciousness, or partiality, and slightly later, glory, fame, or renown. (A shift of stress to the last syllable made it into a common noun for the person possessing the qualities). Since one common use of this word was to sing praise of the Lord, I can imagine a development in Punjabi that jas meant the praise of the Lord.
Preet is obviously from the Sanskrit prIti `love' whose ancient root prI means `to love' and is cognate with the root of the English word friend. So, jaspreet should mean something like `one who loves [to sing] the glory [of God]', a meaning which seems to appear on a number of sites, though evidenciary value of that last clause is little.
I would guess -reet comes from Sanskrit rIti, again an old word meaning motion or course from a root rI meaning to release or let go. Later, it meant, almost exclusively, an established course or custom. So, jasreet could mean `one whose custom is [to sing] the glory [of God]'.
The problem is (a) I do not speak Punjabi, (b) I know that the Punjabi love for popular interpretations, and their folk religiosity, has often tended to reinterpret names. You need to discuss the name in a Sikh name board somewhere. I haven't seen too many people knowledgeable about Punjabi names here.
Please let us know when you find out about yor name.