you should have a waiting period with both McK and Bain to respect. Usually, this is either 1 (good performance) or 2 years (standard). There are also rare cases of 6-month periods. Thus, as a first thing I would verify how much time you have to wait before reapplying for these two companies (ideally via an internal contact that could talk to HR, if available).
For BCG things should be different as, if I understood correctly, you rejected an offer abroad. In that case, I would try to find an internal contact, and have him/her to ask HR whether you could reapply now for the local offices. Chances are they would be happy to accommodate an interview. In case you are not able to find a referral, you can try to reach out HR directly or ask for help via an expert.
In terms of the process it should be equivalent to the previous you had, with the following add-ons for your cover letter and behavioural questions during the interview:
- You should show how you worked on the areas which led to rejection one year ago for Bain/McK
- You should emphasize why you did not accept BCG and are now willing to move there
- Underline general grow/improvements in the traditional key areas (leadership, drive, impact, team work) in the last year
Thus to sum up I would recommend to:
- Verify the waiting period with McK and Bain
- Find an internal contact for all the firms. If you are unable to do so, contact HR or consider booking an expert to help you with that
- Prepare stories on your improvement on both cover letter and fir questions