Hiking Wadi Qelt to St. George Monastery

I second the recommendation to NOT walk the trail alone for more than one reason.
Another concern is the heat- you can expect potentially dangerous daytime temperatures of around 35-40 degrees next week. There is water along the route to cool down but you’ll have to carry lots of drinking water
You can take an Israeli Egged bus to Mitspe Yeriho but you will need a taxi to wait for you at on the road near the monastery to take you back to a bus station. You can arrange an Israeli taxi from Ma’ale Edumim or a Palestinian taxi from Jericho.

Another circular route a bit west on the same stream is described on this link but it does not reach St. George. This area is also patrolled by Park Rangers and might be considered safer (although falling off a cliff would not be a good idea on either route):
http://www.tiuli.com/track_info.asp?lng=eng&track_id=62

A 30 minute bus ride south along the Dead Sea would bring you to the Ein Gedi Nature Reserve where you can hike alone safely (although the same warm weather precautions must be taken).

Wadi Qelt is located in the Palestinian territory, in the Jericho Governorate. Going there with an Israeli bus is obviously not a good idea and it's not safe.

#3 - Why, will she get an ink stamp on her forehead saying she traveled by Israeli bus?

Wadi Qelt may be in Judea, in the Palestinian Territory, or in Never Never Land, but Mitzpe Jericho (where the OP wants to start her hike) is reachable by Egged bus #123 from Jerusalem. A good idea and 100% safe (the bus ride is. Hiking alone is not).

Here's the September 10th morning schedule:
http://www.bus.co.il/otobusim/Front2007/OuterRoutes.asp?StartPlaceName=%D7%99%D7%A8%D7%95%D7%A9%D7%9C%D7%99%D7%9D&EndPlaceName=%D7%9E%D7%A6%D7%A4%D7%94<i>%D7%99%D7%A8%D7%99%D7%97%D7%95&SelectedDate=41162&TravelDate=41162&MinNumLinks=0&MaxNumLinks=0&TransportationTypes=30&SelectedTimeMode=0&SelectedTime=0.2465277777777778&MaxResults=20&Radius=0.002&domain=bus.co.il&UserAgent=Mozilla%2F5.0+%28Windows+NT+6.1%3B+WOW64%29+AppleWebKit%2F537.1+%28KHTML%2C+like+Gecko%29+Chrome%2F21.0.1180.89</i>Safari%2F537.1&Design=2007&FormIndex=0&LanguageID=20

#5 How big is the Never Never Land entry visa stamp? Will they stamp a piece of paper instead? How will the visa stamp impact on my forthcoming visit to my Optometrist & and the fragrant Asma?

#3 And a special thank you for your 31 posts in 30 hours. This is a sterling effort for which the TT should be grateful. Hopefully the Guinness Book of Records will be contacting you shortly.

Don't forget that if you have a Never Never Land stamp in your passport they'll never let you into Lilliput or Narnia...

#3 (catw)

Wadi Qelt is located in the Palestinian territory, in the Jericho Governorate. Going there with an Israeli bus is obviously not a good idea and it's not safe.

===========================================================
The only thing "obvious" is this nonsense you posted. :)

Going with a settler bus inside the Palestinian territory is not safe. Expats working for foreign embassies and international organizations are even forbidden to do so. There are loads of Palestinian buses and taxis going everywhere in the Palestinian territory, they're safe and practical.