I would not bother trying to get sheet music for that (I assume they are not using notation that much, and what they could be using would not be very useful because of the amount of improvisation, access to instruments, and familiarity with that kind of music).

Try to contact:

• Mvsica Romana
• Synaulia
• Thaleia
• Lvdi scaenici
• Kerylos

We don't really know what Roman music sounded like. Those ensembles attempt to recreate something based on what we have: some surviving instruments, depictions of musicians, mentions of music in texts, theoretical texts that tell us about the intellectual framework used back then to deal with music... There are some surviving forms of music notation, but they don't offer that much detail.