I assume your goal is to get a job, since you mention you are changing careers.
I understand you wish to accelerate your learning curve. Make sure you do lots of hands-on work, then, to make sure you know how to do things and have skills in databases. The skills, as they say, pay the bills.
I don't know what your background in computer programming, computer science, or information science / managed information science is. If you have some background into those topics, you might be able to make it into the stuff I recommend below.
Most databases are relational in businesses. Depending on the business, they run different datbases. The two really big ones are Oracle and SQL Server.
I've known a couple of friends who learned databases (and other enterprise software) by going online and reading as much documentation as they could put their hands (mouse?) on the Oracle and SQL Server websites, and for other enterprise software. They went and applied for jobs, had enough business sense / charisma, could read/write American business English well, and were good enough to get the job with little/no experience, and have done very well. It pays their bills, and is a stepping stone to bigger things. You might be able to do the same. Go on the Oracle or Microsoft websites, and grab the documentation. Read as much of it as you can, circle words you don't know, try to find the definitions. Find a local guru (that's the main advantage of the community college, they have smart people with communication skills who can help), and talk with them.
If your a tremendous reader, you could do this in a month.
EDIT:
As to how much "database" knowledge you need to know to get into your master's...
It depends on the program; I'm going to assume your'e going for a professional program and not a academic one. Depending on the master's program, you may/may not need to know databases. Consult your professor or advisor to see if this is something you could tackle right away.
You need to know, ultimately, how to "talk" to a database. Think of this like trying to do business with folks in a foreign country:
You'll need to learn the language (relational databases use a language called SQL; make sure you know how to formulate a basic query (SELECT), and modify the data in the database (INSERT / UPDATE / DELETE)).
Make sure you know the culture (what is a table, what is a row, what is a column, what is a tuple, what are keys (foreign/primary/candidate/alternate/super), what are triggers, what are the normal forms, what is an ERD diagram, what is relational theory)
Make sure you have safe transportation (learn APIs to communicate with the database in C++ and C#. Learn how you can run SQL queries on the database from your app and get resulting data back inside your app. Perhaps learn about ORM tools and how to get/set data that way).
The above is what an intro course covers.