Always been paid by my previous employers. Its a work cost. Why would the employee need to cover it?

1 hour ago, Cloudy said:

A decent employer would cover the cost of the work permit and Non B. Id stay far away from any on who will not. 

To extend on that, it's perfectly normal for an employer to cover that cost by reimbursing the employee--particularly for the B visa.

 

If that's the case, make sure it's clear in your contract that you will be reimbursed and when that reimbursement will happen (e.g., first paycheck, after passing probation).