Is this possible?

I have this microcontroller which I have read mixed reviews about whether or not it has the bootloader installed. Also I have this to attach through usb. When I hook everything up on a custom pcb I go to arduino ide to attempt and load that program but I just get "programmer not responding" when on my mac and "not in sync" when on windows 7. Can anyone confirm whether or not the micro controller has the bootloader or any way I can make it load up with that adapter?

The bootloader is probably missing if you got it from Mouser, they wouldn't waste their time to put on any bootloader. The USB BUB II is the same FT232 chip, so take some hints from the above link

I honestly don't know where to go with that, I am fairly new to this and was just doing a project I saw online however I thought the microcontroller I bought came pre loaded, I do not want to have to try and find a new one and get that.

An ATmega328 cpu bought from pretty much anywhere will not contain the Arduino Bootloader unless the vendor specifically said it contained that bootloader (the chips do not normally come with ANY pre-loaded bootloader.)

So your chip almost certainly does not have a bootloader. To get it to work, you will have to install a bootloader, which requires a tool that supports the non-bootloader programming protocols. I don't think the USB BUB-II is sufficient. Do you have some other working arduino? A PC with a parallel port and some electronics parts?

You're going to have to interpret the Duemilanove schematics to do this. The connections from the FTR232 to X3 and the ICSP header connections to the ATMega328 are what allow the BIT Bang programming via the link above.

Doesn't look to me that the USB BUB breaks out the X3 connections, so you'll have to tack on some wires bring those signals out, while connecting up 16 MHz xtal, 22 pf caps, 10K reset pull up resistor, power & gnd.