Yes. There is no requirement that you fly coach. You can report your travel expenses in turbotax under work-related expenses. There will be a question for non-taxable reimbursement. Enter the amounts reimbursed by the company here. The difference is what you can deduct as as additional deductible expense. However, this is a miscellaneous itemized deduction subject to the 2% rule so your actual tax benefit will be reduced depending on your other tax facts.
