How can I express what I study?
Solution 1:
You'd say "I'm in my third year of studies towards a bachelor's in Computer Sciences" or something similar. Note that it is a "bachelor's (degree)," not just "a bachelor." Your phrase instead means you have your eye on an unmarried man in CS.
Solution 2:
A few examples
I am a third year student of bachelor of science in computer science. (If the broad category is kept)
I am a third year student of bachelor in computer science. (If the broad category is omitted)
I am studying in third year of my bachelor's degree (in computer science).