So a few days ago, I noticed that my brake/tail light was no longer working. Okay, sure, these things happen. Picked up replacement bulbs, installed, lights worked no problem. Today, I noticed the brand new bulb is now burnt out yet again.

What could be causing the problem? I'm kind of a novice when it comes to electrical tech, so any suggestions would be appreciated.

yeah, the bulb is burned out. filament is toast, and theres black on the inside of the bulb. I have one more that came in the pack, though I wanted to see if I should check something else before putting it in.

Your suggestion has merit, Justin. I thought the bulbs looked kinda crappy coming out of the package. Thats what I get for using Autozone.

You called it a "short" which means "short circuit" which means that the positive wire touches the neg somewhere in the system and either blows a fuse from over amperage draw, or smokes the wire.....in the case of a lack of a fuse.
In this case it is not a short. The only thing I can think of causing this, is either a defefective bulb, or a shot of too hi a voltage, meaning a voltage of at least 16-18 volts. And the only thing that could cause this is a defect in the charging system ?? I think I would check your charging voltage first. Excessive hi voltage can be caused from a defective battery also.

JOG hit it...   make sure the brake light isn't on all the time.  If either switch (front/back) is shorted or stuck, that will happen.   In fact, it happened to me down in the Baja on my Harley a few years ago.   My rear brake switch fused in the closed position, causing my brake light to stay on.   Mine didn't burn out, but caused my voltage to drop from 14V to around 12V which didn't charge my battery very well so I had starting problems all the way back to the states.  I had to park on hills, so I could bump start.  I thought I had voltage reg or battery problems until someone pointed out that my tail light was awfully bright.  After that I pulled the bulb and finished riding home in the daylight only.

The tail light is 5W, but the brake light is 21W; i.e., a substantially heavier continuous load on the battery and alternator.   One last thing, those bulbs are keyed to fit in the socket ONE WAY ONLY, but I've seen people force them in backwards on both bikes and cars.   Anytime you see a car with one tail light much brighter than the other, then thats what they did.

I was having a similar issue and it ended up being that one of the electrical wires under the seat was exposed and touching the frame, shorting out when I hit a bump or whatever. Might just pop the seat off and check your wires for any areas of exposure.