It's per attribute that you're checking, you're not bailing on the entire validation process, only on other checks on that particular attribute: From the docs:
Stopping On First Validation Failure
Sometimes you may wish to stop running validation rules on an attribute after the first validation failure. To do so, assign the bail rule to the attribute:
In this example, if the unique rule on the title attribute fails, the max rule will not be checked. Rules will be validated in the order they are assigned.
But that is where the official docs are misleading. Simple check shows that it does not continue validation on an attribute after one of the rules fails. It is even obvious that we would not start testing the value on a table if it is for example fails on integer rule.