Why does my travel expenses still say $0 despite the fact I entered numbers in at least a dozen times? Is there a way to fix this glitch?

Are you a W-2 employee?

Yes

Unreimbursed employee business expenses are no longer deductible under the new tax laws unless you fall into one of the 4 categories below.  This is why you are seeing zero after entering your mileage for your federal.

A few states still allow this deduction.  If you are in one of those states you will see it on your state return.  

"You can no longer claim a deduction for unreimbursed employee expenses unless you fall into one of the following categories of employment, or have certain qualified educator expenses.