You have given the right information, but now it is time to go a step further. Here are some tips to think about with blue screens:
Do you think it is possible to get to c:\windows\minidump\ before the system crashes again, and get the .dmp files in that folder? Hand them off to a USB flash drive or e-mail them to yourself? Post them here? These are memory dump files, which allow for diagnosis of the problem in the most direct way through Crash Dump Analysis.
Did anything in the environment of your computer change prior to this happening? As you have said, you've only had the computer for two months, and during this time frame, if anything is going to go wrong, it would go wrong early into ownership. When thinking about any notable changes, please think about whether or not you installed a new software program, made a change that might have seemed arbitrary at the time, etc. For example, did you just install new anti-virus or firewall? Did you see something strange on the screen and become dismissive of it prior to this happening? If you can think of something specific, this will help us come up with a better hypothesis of what is going on.
Are you able to collect, remember, or even take a photograph of the blue screen message, as it appears, on the screen? This would be helpful in that we can understand what this "bird" is. I for one have never heard of such a thing, it certainly is not part of the Windows programming, to my knowledge, and you should not be seeing a "bird" in a BSOD. What is most important will be the error code and stop code, as well as any file references being made in the message.
BSODs are crash dumps, and are a way of the system telling you exactly why its crashing, before it actually does. Its the last message saying, "Here's what made me crash" and this information is outputted to c:\windows\minidump. Specific tools are used for analysis of these files, but information on the screen itself, including the STOP code and error message could be very valuable, especially since you cannot get into the computer.
We should not start to jump to conclusions about what is wrong until we can get more information firsthand. If any drivers were updated, and so on, try booting up with F8 and using "Last Known Good Configuration". The fact that you are getting them in safe mode is not a good sign. More information is needed to determine a course of action, but you may want to try contacting your computer manufacturer. At 2 months in, you are may be covered with an extensive warranty on the system. Please see if you can provide this information, as I now move this to our BSOD forum.