New York requires employers to report income earned everywhere on the W-2. The New York section of TurboTax allows you to allocate your wages and report the correct amount.

You only have to pay tax to NY on income you earned while living in NJ.

• In New York, go to New York Income Allocation
• Say No to "Were all of your wages and/or self-employment income earned in New York State?" 
• Say NO to Did you have any New York State Wages?
• On Tell us about your New York resident income enter the amount you earned while living in NJ and working in NY
• On Tell us about your New York nonresident income enter $0

Thanks for the response.

Am I correct in assuming that the bonus paid in December while I was a resident of TX would need to be apportioned to NY also, or would I only need to report income that was actually received while I was a resident of NJ?

You are correct.  For NY the bonus is allocated the same as the wages.  You will use the total pay (including bonus) and allocate by days or percentage to NY.  You should claim a credit on your NJ PY return for taxes paid to another state for the NY taxes.