'Baccalaureate' is not correct as this is an exam taken at the end of secondary school studies that qualifies for university entrance in France. I think 'undergraduate studies' is fine for BE speaking readers too.
Yes, there is also the 'International Baccalaureate' (taken in some English-speaking contexts including the UK) which is an exam taken by pupils before entry to university. Using the term for undergraduate studies would therefore be very confusing.
I agree with cyberpedant that 'Bachelor's studies' is unidiomatic. 'Undergraduate studies' or even 'Bachelor's degree' work better.