Fledgling magpie in garden...with a dog!

Hello! 

We found a wonderful fledgling magpie hiding in the undergrowth in our garden three days ago. The parents are on a neighbouring roof and swooping well.

My worry is we have a dog who is getting suspicious! The fledgling is becoming bolder and sauntering away from the undergrowth. I always go out and create some noise, making sure it hides before my dog is let out, but the bird has started to come out from hiding when my dog is still out there and I am worried! Keeping the dog in permanently is not an option, but I am doing all I can to ensure she is supervised. 

My question is how long do fledglings remain grounded? I read somewhere on the internet that it is 4 months, but hoping that is not true!!???!