They hire non-US citizens out of undergrad or MBA but their sponsorship policy is the worst when compared to McKinsey/BCG or do largest banks they compete with most of the time.
Bain only applies for H1B visa once, and if you don't get it they will not re-apply, while most other consulting firms will offer to re-apply.
Bain's policy is to send you to an office abroad (you have no choice in selecting it, it's rather selected on demand) and then you are brought back on L1 which ties you to the company for as long as you stay in the country. This means that if you don't get promoted or want to leave, you need to leave the US.
Although they could apply for H1B which gives you the optionality to work at other companies in the future in the US, they won't do it. This means that as an international you are not allowed to use opportunities such as externships that your other peers are able to do.