In the end, Asp decided it would simply be easier to bring Jonathan to the Circle of Creation. He was a friend of Sharp's and thus a friend of the Arrow - and any Arrow could find out the location of the Circle. There were plenty of private spaces in the area. Better here than to bring someone she'd just met to meet the Threats and reveal their Sanctum's location.
Star and the girls would probably just make fun of her anyway, when she wouldn't tell them what this training was about.
Why was it that she chose a story about dojo sex, again?
"Welcome to the Circle of Creation," she said as she led Jonathan into a quiet space. "It's the Arrow's local HQ. Plenty of space for us to train privately. So, is Jonathan what you prefer to go by in Awakened company?"
Introductions. They were a thing (small T).