Correct me if I’m wrong, but I think the timeline so far looks like this, from my recollection of the episodes and some online summaries:
Ep 1, Rachel shows up at the police station after dark, gets kidnapped and rescued, and Dick takes her from Detroit to DC (about an 8.5 hour drive), with an overnight stop (pizza, no pineapple - Rachel watches GoT and snoops on Dick’s fancy computer). Meanwhile, Beast Boy is in Covington, OH stealing video games.
Ep 2, IIRC, they stay one night in DC with Hawk and Dove and Dove (who should be able to fly but apparently can’t - which makes me worry about how comics-faithful Kory and Donna will end up being) gets thrown off the roof of the building after dark, and Rachel goes on a road trip with Nuclear Fam.
Ep 3. DC to Chicago is 10.5 hours, but somewhere in between Kory roasts Dad and heads to the Convent (presumably close to Covington ) DC to Covington is about an 8.25 hour drive (plus other lost time investigating) for Dick, assuming he’s not counting on the brass pass to get him out of trouble, out of state. Much of the day passes by the time Rachel escapes the convent.
Ep 4 seems to pick up directly from Ep 3, and chronicles the rest of the day, Dinner happens, then crazy-medical-stuff and Rachel puts Chief back in his wheelchair. The Titans leave well after dark, fairly late in the evening.
Ep 5 has them driving through the night to somewhere, Dick trading in the Porsche the next day, getting a crappy hotel room, testing powers, and then Dick and Kory testing the mattress back at hotel-craptastic. Shortly after nookie-time, Nuclear Family attacks. Another night passes, and Dick shows up at Adamson’s place in Chicago the next day. (Covington to Chicago would be about 4.5 hours - anyone remember where the hotel was?) Nuclear Family go boom, Robin rescues Robin,
Ep 6 picks up where 5 left off, and Robin and Robin go to the safe house, the rest of the Titans show up sometime later, R&R go off to chase down Zucco Jr. and that adventure clearly lasts at least well into the night/early morning hours.
Ep 7 starts in daylight hours with Dick back in Chicago, then off to the Asylum, wherever it is, and the ep ends at night.
So, about 6 days, maybe 7?