Sadly you are not going to be able to do what you want simply connecting CAN-H and CAN-L to a serial port. Here is a pointer to the physical interface layer for CANBUS.
CANBUS Physical layer ISO 11898
What you will find is that while CAN is a "serial bus" that just means that the data is transmitted one bit at a time. It does not mean that it can be connected to a serial port. The serial port on your PC or the one on a USB to serial adapter require RS-232 input levels. CAN is roughly 2 or 3 volts and not the +3 to +15 or -3 to -15 required by RS-232. In addition the serial ports require a start and stop bit with 8 bits of data between them. That's not at all how data is transmitted on CANBUS.
What you need is a evaluation board for a CANBUS transceiver which will likely have an output you can connect to a PC via serial or USB.
To help describe this, here is a diagram of the standard architecture for these kinds of system:
Your PC would have to be at the other end of one of these connections on the "CAN BusLine" and hence would need an embedded CAN controller to talk to. The device you're trying to test will have a matching stack inside it, and you need one connected to your PC in order to talk to it. It's all possible by finding an evaluation board for an embedded CAN controller who's interface is serial or USB.
Hope that helps!