No, Gandalf rode together with the company to Bree1.
When Barliman Butterbur says "...first set eyes on him", he is talking, as Daniel has pointed out below, about when Gandalf rides to Bree in search of Frodo, after escaping from Orthanc and passing through Rohan.
21 Gandalf meets Shadowfax, but the horse will not allow him to come near. He follows Shadowfax far over the fields.
22 Gandalf overtakes Shadowfax.
23 Gandalf having tamed Shadowfax rides from Rohan.
24 Gandalf crosses the Isen.
27 Gandalf crosses Greyflood.
28 Gandalf reaches Sarn Ford.
29 Gandalf visits the Gaffer.
30 Gandalf comes to Crickhollow, and reaches Bree at night.
The Return of the King - Appendix B: Tale of Years - 3018.
From the above, it would appear that Barliman first saw Shadowfax 9 days after Gandalf had acquired the horse, just after Frodo's departure. However they would've had more pressing issues to discuss than the beauty of the horse.
5 Gandalf and the Hobbits leave Rivendell.
6 They cross the Ford of Bruinen; Frodo feels the first return of pain.
28 They reach Bree at nightfall.