How can I be shipped to BLC quicker?

Make sure you have completed your SSD-1 and work on maximizing your promotion points so you can get promoted as soon as possible.
Additionally, make sure you're administratively ready, keep your APFT, HT&WT, Medical/Dental, Records Review, DA 5960, DD 93, SGLV, and ARB updated every year and keep your availability open. Have your leadership work with the training NCO's to work you in if anyone drops out last minute and they need to fill a class seat.

Get your promotable status and it will put you at the top of the list for BLC

Being in the National Guard it'll depend on multiple things. First off being, are you even eligible to be sent? By that I mean, do you have time in grade? After that you have to think of who else within your unit is eligible to be sent to BLC, and that you may not be high placement with that. Finally, the biggest obstacle is whether or not your unit has actually been given a seat in a BLC class. This usually comes down from battalion or whomever, as they're usually granted a handful of seats to disperse among their down trace units.

I digress though. You as a soldier need to ensure that you're standing out by surpassing the standards in APFT, weapons qual, etc. Prove to your leadership that you're up to the task by volunteering to "lead" small tasks given by your first line leader. There are many things you can do to increase looks from higher, but ultimately getting into BLC is dictated by logistics.

Since you're in the Guard the following point might be relevant to your situation.
https://www.rallypoint.com/answers/does-promotion-in-the-guard-come-slow

Stay vocal about your desires to your leardership and touch base with your training NCO to be aware if slots open up. Got my slot of 2 weeks notice cuz sombody failed HT&WT.
But on a side note, know your job, know your role and if you can know the role/job of the person above you. If your actions inspire others to dream more, learn more, do more and become more, you are a leader. Its important to be green on medpro's, have good APFT, weapons qual, required training completed, etc. All that is expected of you. Being an NCO means being a living example of professionalism. As an E-5 you will be the most directly ifluential and present leader to alot of the soldiers around you. If your going to BLC it should mean you already possess these qualities. To me BLC doesn't create leaders, it simply gives them another exprience to learn from. Hope that makes some sense.

contact local school house and see if they have any walk - on seats available

Go Active duty.

As long as your in the primary zone your name should be showing up on the list if you want to go before take the time and get your packet completed and put in the school request. Walk-on's happen all the time if that's not enough get P status and put in the packet again. Your sure to get picked then good luck.

Volunteer for and apply for BLC in route to your next duty station. This way. The funding comes out of Army general funds instead of installation funds.

Your best bet is to speak with your supervisor during your monthly or quarterly counseling he or she should be able to let you know whether you are being considered and what you can do to get prepared. Thank you for your service.