My ears are burning....
What you need to acheive is lighting the background 1 to 1.5 stops brighter than the subject. You can do this with direct and reflected light, but it's much harder than with strobes. If you have one or two hotshoe mounted strobes and a way to fire it (them) remotely, you could use sunlight for the subject and the strobe(s) for the BG. You will have to either use spot metering or go full manual to have the subject exposed correctly and let the BG get close to blown out. Make sure she isn't wearing too light a color clothing or she will disappear into the BG. Strive to keep detail in the subject, but let the BG get close to 245,245,245. You can also shoot her in a bit of shade (like a tree or scrim), use a strobe for fill, and use the natural sunlight to light the BG. Shoot her wide open and let the BG overexpose.
Keep her at least 6 feet from the BG too so that your DOF will lose any detail in the BG. That also helps to reduce or eliminate any shadows from the key light on the BG.
Hope this helps.
Let me know if what I posted isn't clear or you have other questions.
