Very good question, and great to see that PhDs also consider consulting!
To be honest, I don't believe there is any standardized position for PhDs as for instance "Summer Associate" which you have for MBAs. This will mostly depend on:
- Which country are you applying for?
- Is your PhD in an area relevant for the given firm?
BCG and McKinsey are building specialization earlier than Bain, so if they need in your region/office an industry hire from a specific industry, you will definitely have a chance (you would then have a similar position/role as a summer associate)
I am assuming that Bain will less give weight to your area of expertise, but I might be wrong as they will highly depend on the office/region you are applying to.
In anycase, I would suggest as next steps:
- Keep in touch with MBB consultants via linkedIn/social networks in your region/office
- Find out if there is a need for industry hire in your field
- Prepare for case interview as if you would be applying for a summer associate position
- Send your applications not depending on deadlines but more of the companies needs: landing an internship as a PhD is not common and it will be a lot a matter of timing
I wish you the best of luck and don't hesitate to reach out if you have any questions!