Our Programming for Evolutionary Biology workshop is about 3 weeks long: http://evop.bioinf.uni-leipzig.de/ . I can assure that organizing just these three weeks requires quite a lot of efforts and commitment. I couldn't imagine the stress of organizing a three months course :-)
I don't think that there are 3-months long bioinformatics courses, but there are some very good data science bootcamps. See for example:
http://www.thisismetis.com/data-science or http://www.skilledup.com/articles/list-data-science-bootcamps. Google Summer of Codes also take about that amount of time, although they are usually done from home.
I also think that 3 months is too short for a internship, but if you contact many universities or industry I am sure you will get some positive answer. Specially if you can provide your own fundings.