First year science at UBC is pretty packed and you don't generally have a lot of space to take extra courses. I would also recommend contacting the science advisor for help/questions about your first year, as they are very helpful and can provide the most accurate advice.
That being said, I was a student at UBC before BCIT and can help you out a bit
For UBC science you will need to take both BIO 112 and 121 (and 140, the lab). You will need to take CHEM 121+123 (or 111/113 if you haven't taken chem 12) AND two classes of physics (sorry, I did not take physics for my program so don't know much about them).
BCIT looks for you to have 3 credits (one course) of English. This is also required for first year UBC science, so that isn't a problem.
BCIT also looks for you to have 6 credits of psychology or sociology (2 courses). You might be able to fit that in your first year timetable, or you could take it in the summer or second year. They also want you to have 6 credits (2 courses) of 200+ level Arts electives. So I would recommend taking PSYC 100 (6 credits) and then two upper level psyc courses.
If you've taken BIO 12 in high school, that is all BCIT requires. However, I do recommend taking BIO 153, as it will be very beneficial for your nursing courses at BCIT. It is a 6 credit (year long) anatomy and physiology course, and goes in depth into a lot of what you learned in BIO 12. It will without a doubt help you when you get to BCIT and take patho! However, I don't think you have room in your first year timetable for this course (and it is very demanding, so I don't recommend squeezing it in). Perhaps you could take this in the summer, or in second year.
Let me know if you have any more questions