Many of the tools that were viable when this question was first posted have become abandonware.
Clonezilla is an enduring option. Some (including me) find it cumbersome and sometimes confusing. Systemback is more user-friendly. There are multiple tutorials for both. Distroshare is another option. There are also paid options that I have not tried (e.g., TeraByte, possibly PowerISO).
I will mention some other possibilities, in case the ISO route is not really your best solution.
First, I suggest thinking of backup and copying as two separate processes. Backup should occur regularly -- maybe monthly, if you don't make many changes to your system drive. Your best backup method may or may not be the same as your copying method.
For copying, there are at least three basic approaches:
Connect drive B directly to drive A. This is feasible, even on laptops, if you can get drive B out of its machine: you can connect it to system A using an external docking station (assisted by male-female SATA extension cord if necessary).
Start with an image of drive A. You may or may not find that the imaging process gives you the kind of monthly backup you want. Use the image to restore the system to drive B.
Make an ISO of drive A. The ISO will function as you say: install it onto a USB drive, boot system B with that, and use that to install onto drive B.
There is further information on those possibilities, in case the ISO route is not, after all, the one you want.