Often internships are aimed at penultimate year students, so for those on a 4 year MSci you would undertake these in the summer between 3rd and 4th year. Some may be open to students in any year, you may just need to look further afield for those. Any internship is better than nothing.
Note also you don't "get a bachelors" then "get a masters" on an MSci course. It's a single coherent degree where you get the award of MSci after 4 years. There is no degree or qualification awarded between years 3 and 4 in the same way as you were not awarded a qualification between years 1 and 2 or 2 and 3, unless you withdraw from the course and receive an exit award.
Therefore you would not be doing the internship "after getting [your] bachelors" because that's simply not how the qualification works. You won't be graduating from anything at that stage or earning any qualification unless you leave the programme early at that stage effectively.