The NASB is based on the 26th edition of the Nestle-Aland "Critical" Greek text. The Greek text only contains a single instance of λατρεία (latreia):
Παρακαλῶ οὖν ὑμᾶς, ἀδελφοί, διὰ τῶν οἰκτιρμῶν τοῦ θεοῦ παραστῆσαι τὰ σώματα ὑμῶν θυσίαν ζῶσαν ἁγίαν εὐάρεστον τῷ θεῷ, τὴν λογικὴν λατρείαν ὑμῶν·
Probably the NASB chose the words it did to distinguish between λατρεία and the other Greek word often translated as "worship"- προσκυνέω (proskuneō).
Laurent Cleenwerck wrote extensively on the difference between λατρεία and προσκυνέω in the introduction to his translation of the Orthodox Patriarchal Text, New Testament: Eastern/Greek Orthodox Bible:
In modern English, “worship” (like prayer) has mainly taken on the meaning of an act (invocation, prostration) offered exclusively to God. However, the original and official semantic range of this word used to be much wider, as was the case of the Greek word προσκυνῆω (proskuneo) which is normatively applied to God but also to human beings [Genesis 27:29 LXX, 1 Kings 1:16 LXX, Revelation 3:9]. The idea conveyed by proskuneo is that of “offering obeisance,” “making a physical demonstration of veneration and respect” or “prostrating oneself.” With this in mind, the New American Bible sometimes translates proskuneo as “to do homage,” including when applied to Jesus.
In contemporary Eastern Orthodox terminology, the equivalent of proskuneo is often “venerate.”
With this background in mind and taking into account the current, narrow sense of “worship,” the EOB has opted to always translate προσκυνῆω (proskuneo) as “to express adoration” with a consistent explanatory footnote. This approach faithfully conveys the meaning of proskuneo by combining the idea of a physical (or mental) expression with the broad sense of “adoration/to adore.”
Latreia is always rendered by the expression “to offer divine service.”
As Romans 12:1 demonstrates, the NASB editors took a similar approach with respect to latreia. The word, which appears five times in the New Testament, is translated as "divine worship" in Hebrews 9:1,6; "service" in John 16:2, and Romans 9:4; and "service of worship" here in Romans 12:1. The NASB seems somewhat looser with regard to proskuneo, which is translated simply as "worship" in the vast majority of cases (52 of 60 appearances), but also "bow", "bow down", or "prostrate" in some cases.