can I come back home with you?

[flytothesky]

Hello~ Can you help me say this naturally please?

(A and B are flate-mates)

A: Would you like me to drive you at Uni?

B: What a nice offer, thanks.
Hey, what time are you going to come back home?

A: Around 9pm.

B: That’s great, can I come back home with you?
can we come back home together?
Because I have night class and there is no school-bus at that time.

A: No problem, I will see you at 9pm at the security center building.

[Soup]

A: Would you like a lift to Uni?
B: What a nice offer, thanks. Hey, what time are you heading home today?
A: Around 9 p.m.
B: Me too. Can I get a lift home/lift back with you? I have night classes and the buses don't run that late.
A: No problem. See you at the Security Center building at 9 p.m.