Without being facecious -
1) Remember you NEVER STOP LEARNING!
2) Buy Books on the subject and on the tools you are using. READ them all from cover to cover. Make notes in the margins and use POST-IT notes to mark sections of special interest.
3) Find a more experienced DBA and have him/her mentor you.
4) Quit when you stop enjoying it.
The full range of skills needed to become a proficient Senior DBA do not appear in any book that I have read so far.
The basic skills you should have been taught during your BSc. Refine these findamentals with practice and experience.
Think about taking an MSc. This should broaden your exposure to the skills required in the IT fields and open up to a number of new concepts.
THEN you begin the real learning.
Currently IT skills are an art form. Developers get taught a certain range of skills at college / Uni, but some developers 'know' how to code. They have an aptitude for what is esentially a creative task. If anybody could be taught these skills to that degree then there would not be the skills gap and we would not be paid nearly so much as we are now. :(
Getting into a company with an established Senior DBA who is willing to teach / mentor is an important objective. 25 years ago there were very few Senior DBA's and I had to learn by trial and error. Occasionally making mistakes that would not be tolerated now (I bought the whole company to a stand still for a whole day once; try doing that now-a-days and keeping your job.)
My previous comments are still valid. I buy 4 to 8 books per year, read them ALL, from cover to cover. And I note and experiment with the things in the books. Currently to my right are two books on PHP. I have about 6 books on PHP. Each one gives a slightly different view point and I learn different things from each.
I will repeat thet IT skills are basically creative. If you have a talent for IT, your skills will improve, even if you do nothing but just your day to day work, you will gain experience.
I wish you luck and hope that you have at least half the fun that I have had in this business.