Yes, it is correct. In the past, there was a difference. Both learners of English and native English speakers used to be taught that 'may' meant permission and 'can' meant physical ability. There are still pedantic people, taught by teachers using grammar books written around 1950, who insist that if you want to ask permission you have to use 'May I ...?'. However, this does not reflect the reality of how the language is used today. Nowadays, 'May I go?' and 'Can I go?' are actually used to mean exactly the same thing. They both mean 'Is it possible for me to go?' The 'may' form makes it crystal clear that you are asking the person's permission, but in fact this is rarely used these days. It can sound over-formal and old-fashioned. In this day and age, it is fine to ask permission by saying 'Can I...?'

In general - 'can' is more universal. It can be used either for asking permission, or for asking about possibility. 'may' can only be used for permission, and tends to be more formal and/or old-fashioned. So - in your example, if you are asking permission, such as from a parent, boss, or teacher, then yes, either is possible. If however, you were asking about possibility, such as if someone was fixing your car, and you were asking if it was possible to leave now, then you should only use 'can'.

To be clear: If you want to ask if something is possible. "Can I go there by bus", only "can" is correct.

"May" may be used rarely these days, but I still use it. Usually when asking a food server or someone behind a counter for something. Maybe it's old-fashioned but I'm still teaching my son to use it, so maybe it will hang around for awhile.