Slow algorithm to insert strings into indexed file in alphabetical order

Hi guys,
this is day 17 out of 100 days of code in go lang.

Today I have played with files, sorting, bytes and strings. The goal was to create a kind of indexed file where all lines are arranged alphabetically.
What I got is very slow algorithm which took 15 seconds to insert 10K strings in an empty file and 49 seconds to insert another 10K strings to the same file. So, it slowdown very quickly as size grow.

I have to convert between strings and bytes which was kind of annoying, but maybe I am doing it wrong? Please let me know in comments.

If you want to load test it here is how:

Source code at Github

Happy coding!