I need your help.
is there a difference in meaning between
May I use your bathroom ?
Can I use your bathroom ?
'May' is more correct, as it is asking for permission. 'Can' literally means 'is it (physically) possible?' but is often used in this way by native speakers and would not be misunderstood or sound at all strange. 'Could I use your bathroom?' is another alternative - maybe a little more polite and formal. All three of these are pretty much interchangeable to my BrE ear.
Most commonly, they would be taken to have the same meaning: A request to use a bathroom.
It is possible for can to have meanings other than asking permission (e.g., asking about ability or possibility). These alternatives can be found in dictionary entries under the word.
In addition, some people consider it completely unacceptable to use can to ask permission, at least in formal writing. In 2009, less than 19% of a large panel of US academics, writers, editors, etc., considered this use of can to be completely unacceptable.
There is an informative brief on this topic under "Usage Note" here.