I’m self employed and make around $35,000 a year. How much federal and bc provincial tax should I hold back from my pay.

The amount of taxes you would need to pay would not just depend on your income, it would also depend on what credits & benefits that you are eligible for. 

You can use TurboTax to create a mock return that will give you an idea of what you might owe. Or you can use the TurboTax Canada Income Tax Calculator for a quicker estimate.