How to connect breakout boards to bread boards?
One way that might work is to use clip-on or "grabber" test leads:



You can find these inexpensively on eBay or from electronics suppliers. (I found the image at Circuit Specialists.)

On the breadboard, insert some pin headers or just use some short jumpers to clip the lead to.



Edit:

In response to your edit, putting the PCB on a 1x7 header would work if


You are soldering the pin header to the PCB. If it's loose, you'll be fighting loose connection issues.
The holes on the breakout board are spaced at 0.1 inch, matching the pitch of the breadboard and header. (It doesn't look like they are, but I could be wrong.)