That’s what I’d do.
Tell them the rest of the system has been bled. And all you need is to have the ABS pump bled.
Tester
I looked at the factory repair guide I have for my Mazda and the procedure for flushing the brake fluid does not mention anything about the ABS, just old school pumping and filling/etc.
If the OP is going to have someone bleed the ABS pump would it not make sence to just have them do the whole system . I think a mechanic would be reluctant to just do part of a brake system for liability reasons.
No.
Once the primary brake system is bled, all that needs to be done is to bleed the ABS system.
That’s what makes it hard for the shade tree mechanic to bleed the brake system properly.
Tester