I feel that Tom didn't want to appear to help the hobbits too much. He wanted to keep them safe, hence the litle song, but he didn't want them to become dependant on him, so he didn't accompany them.
The hobbits needed to grow. So far, they had relied on others when they got into trouble: Gildor, Farmer Maggot and Tom. On the Barrow Downs, Frodo found the strength to act for himself in tacking the Barrow-wight. Tom, by letting make their own way to Bree, was giving them the opportunity to become more confident and self-reliant.
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