My wife heard this the other day.

Problem:
“Tomorrow” is an adverb, so preceding it with the preposition “on” is incorrect.

Explanation:
“Tomorrow” already tells you when.

For example, the answer to “When will they leave?” could be “They will leave tomorrow.”

In contrast, “Monday” is a proper noun, not an adverb, so the answer to “When will they leave?” could be “They will leave on Monday.”

In other words, the days of the week, which are proper nouns, require the “on” preposition to tell you when, whereas “tomorrow” already tells you when.

Solution:
“I’ll bring that to you tomorrow.”