Can holding a baby's face while burping them cause bruising?

An unusual question.

In a way, a reflex or muscle spasm MIGHT have caused bruising in this circumstance. However it's quite unusually difficult to cause deep bruising like this.

If you are worried about bruising on a baby or child, you should always contact child specialist authorities (through the police maybe), for the child's welfare and safety. A specialist can determine the cause of injuries to a child.