the lord of the rings - How often did Gandalf return to Hobbiton after the events of The Hobbit?

It has been a while since I read the Lord of the Rings novels (don't have a copy at the moment) but I seem to recall he went to Hobbiton at least once, as the young hobbits were always excited to see him.

Did he travel there often?

Answer

Not exactly often

It was certainly often enough that he was known to the hobbit-children when he showed up for Bilbo's party in T.A. 3001, sixty years after the events of The Hobbit (emphasis mine):

They knew [Gandalf] by sight, though he only appeared in Hobbiton occasionally and never stopped long; but neither they nor any but the oldest of their elders had seen one of his firework displays - they now belonged to the legendary past.

^{Fellowship of the Ring Book I Chapter 1: "A Long-Expected Party"}

We're only told of one specific visit between The Hobbit and Bilbo's party, in T.A. 2949:

2949 Gandalf and Balin visit Bilbo in the Shire.

^{Return of the King Appendix B: "The Tale of Years" (ii) The Third Age}

However, presumably he visited at least a couple of times each year; a later entry tells us that Saruman begins tracking Gandalf's movements, and notes his particular interest in the Shire:

2953 Being jealous and afraid of Gandalf [Saruman] sets spies to watch all his movements; and notes his interest in the Shire.

^{Return of the King Appendix B: "The Tale of Years" (ii) The Third Age}

After Bilbo's party, he visits Frodo in T.A. 3004, and then only a few times over the next four years:

3004 Gandalf visits Frodo in the Shire, and does so at intervals during the next four years.

^{Return of the King Appendix B: "The Tale of Years" (ii) The Third Age}

Gandalf's travel schedule being so erratic, this is about the best we can do.