The offset may indeed be different from task to task especially if the area is hilly/mountainous. (depending on the context) For more consistency across larger areas it can be beneficial to align the highways which will run through other tasks so that a consistent alignment can be achieved. This works well when the area is quite flat. Remember to add the offset to the comments as the first thing you do after locking a task for mapping; I've certainly forgoten to state which sources I used and their offsets on a few occasions. It's easy to forget if everything already looks aligned. 

You can use the arrow keys at the sides of the offset box for fine adjustment.

In JOSM if you have any questions pressing F1 for context help tends to work well, otherwise check JOSM forums/chanels, or ask. In order to replace geometry you need to install the "utilsplugin2" plugin via preferences (F12) then plugins, search for it and download it. you can click the more info link to see what other functions it enables. You need to replace before you upload by selecting both features and using the shortcut; it doesn't work on features already on the OSM servers. 

One thing I forgot to mention is that the situation in this area has changed significantly so only a few features may be common between ESRI and Bing, but it can still be useful.