As noted,
Gandalf went south to meet with
the White Council of which
Saruman was the leader. The business with the
orcs in the crossing of the
Misty Mountains and the group's time with the
eagles may have caused him to consider what was happening in
Middle Earth at that time. Furthermore, I do not think he wished to enter
Mirkwood because he did not want to attract the attention of the Necromancer in
Dol Guldur which was located in the southern part of that great forest.
I also wonder if Gandalf was already speculating about
Bilbo's unusual behavior (escaping from the
orc den and apparently "sneaking unseen" into their gathering). He definitely had questions on the above and may have decided to see if there were anything else that might shed light on the matter. He does, however, mention his discomfort when he learns while in the South that the road through Mirkwood no longer ran completely through but ended in deadly
marshes. I believe when he learned this, he turned around and began to head back to the group - although this must have been AFTER his meeting with Saruman and the rest of the Council. (Interestingly enough, the White Council included
Galadriel and
Elrond, neither of whom would have been physically included since they did not leave their respective homes. How then, did the "Council" meet? I don't really know.)
Indeed, I have always wondered why Gandalf bothered to get involved in the
dwarf business at all even though
Thorin had asked that he choose the fourteenth member (to avoid a group of thirteen which was considered unlucky). Might Gandalf have wished the attention of the powerful of Middle Earth to be attracted to what was going on in the
Lonely Mountain with the
dragon (always an eye-catcher) rather than take note of what HE was doing?