I am working with OpenLayers plugin in QGIS 1.8 but I am not sure on how should I manage the CRS.
The default CRS for Google/Bing layers is WGS84/Pseudo Mercator (EPGS:3857) but I am not sure on the CRS of the new layer I want to work on.
You should create new custom CRS and assign it to your layer(s). This quick and dirty approach worked for me after reading all the posts arround here. I use QGIS 2.8.1 and metric system, as I live in Central Europe:
Measure your x and y difference between specific point on Open Layer and that same point on your layer
Go to Settings, Custom CRS
Maybe picture is more informative, so I attached one. Hope my approach will work for you as well.