Depending on how you configure the guest OS' network settings, from the network's perspective, the guest OS will just be a separate network node apart from the host OS. I use VirtualBox, and with proper settings, the guest OS just gets another DHCP address and talks to the network like a separate physical computer.
However, by default, VirtualBox uses the host OS as a NAT device, so all network traffic routes through the host OS. Not sure how VMWare works, though.
Either way, the host OS will almost certainly be generating some network traffic, even if the guest OS is logically separate. So, to answer your question, a native or live session of BT will almost certainly be "quieter" than a VM install (but I could be wrong ).
I personally prefer a persistent USB flash drive install with encryption. It's physically separate from the host, easily portable to almost any machine, secure, easily disposable, and only somewhat slower than a HDD install.
I haven't tried it before, but it seems at least theoretically possible that you could use a USB Wi-Fi adapter to connect to a network from within a BT VM, with the host OS having no such connection. Guest VMs have direct physical access to USB devices, whereas built-in hardware is abstracted through the host OS. Now I'm curious to try this!