Doing the BCS self-study course should help.  Once you complete the course, go ahead and apply what you've learned to your current project.

Here are a few more ideas of what you can/should do to increase your chances of landing a Business Analyst job:

• Since your current position already requires you to perform requirements gathering and writing technical specifications you should get even more involved in those activities - volunteer for them,
• If there is a piece of the project which you can "own" from the requirements perspective that would be the time to setup a meeting with the client/stakeholders and perform requirement elicitation (what are their problems, what do they expect of the system, etc.) -> this will be the "requirements discovery workshop),
• If possible, prepare in advance for that meeting and create a list of questions and issues that you are planning to discuss,
• Once you have gathered the requirements, document them in a requirements document and have the client/stakeholders review it for accuracy,
• If you do all of the above, change the title on the resume to something like Business Systems Analyst/Developer or Programmer/Analyst,
• Find an experienced BA who is willing to mentor your (you should start with your local IIBA chapter),
• Work on improving your communication skills both verbal and written.

Here are a couple more resources which you may find useful:

Blog Entry: From Developer to Analyst

Forum Thread: Bank ATM Example

Hope this helps!

- Adrian

As far as requirements go, you might also want to take a look at this book:

Software Requirements, Second Edition by Karl Wiegers

and

The Software Requirements Memory Jogger by Ellen Gottesdiener

The best way to learn is to practice... so volunteer to create these documents and practice, practice, practice...

- Adrian