Is networking not fun
If you power up a computer on the network, the computer may still wake up as well when the computer broadcasts that it wants an IP from the routers DHCP server.
There are lots of features on modern cards that are supposed to allow the computer to sleep through such things. So I guess there may be some trial and error under different situations.
Glad you seem to have an idea of what the problem is. Next step may be to see if Bell has any way for you to change options on there modem.