I'm retired and will be drawing a pension. I have some money in my 403b. The company wants me to come back work part time in 2019.
How many hours can I work and keep from putting me in higher tax bracket?
The tax bracket is unrelated to the number of hours you work.
You need to look at your total taxable income, and your deductions, and the difference define the tax rate.
Note that there is a common misunderstanding of tax brackets - if you reach the border of a tax bracket, any further income is taxed higher, not all your income.
For example, if you get 20$ per hour and pay 10% = 2$ tax on it, and you reach the 12% tax bracket, the next hour you work will be taxed with 12% = 2.40$, all previous hours will not change.