Amman to Petra - Single Woman - Best Method?

Shared mini-bus is the cheapest way. Did not see any foreign women on it, but there were a couple of local women taking the bus alone so assume it is fine. Get your hotel to sort you out a taxi to the bus stop. The taxi driver will drop you off by the buses for petra and you just go and pick one you want. It will leave once full. Will drop you off within walking distance from most of the hotels in Wadi Musa.

Jordan is a very safe place. Just be respectful of the culture and you should have no problems. I even saw female tourists wearing "unsuitable" clothing (short shorts, vest tops etc.) who recieved nothing worse than a few odd/unimpressed looks.

daily JETT bus (aircon targetted at tourist) leaves Amman at 6:30am, arrives in Petra 9:30ish, and returns around 4PM. I reckon you shoud be able to buy the return portion of the ticket for a day or two later.
BTW, if you will have five days in Jordan, get the recently published Roughguide, or at least a pdf chapter of Lonley Planet middle east book. Very useful both.
Enjoy the trip and greetings from Poland!
Pawel

I travelled with my girlfriend in Jordan for 2 weeks and we met up with quiet a few single female travellers .

Jordan is a safe place for you to travel as a solo female. It is nothing like Egypt and Morocco. Any option will be safe. A backpacker bus from your hotel/hostel sharing with other travellers, Local bus or hiring your own taxi/driver. Met solo females who did all of these who had no issues, only helpful people making sure they were Okay and going in the right direction.

I would do a day trip out to Jerash also. And if you have time a dip in the Dead Sea.

Only sight see in Amman for 1 day, the sights are better outside the capital.

Have fun

I travelled with my girlfriend in Jordan for 2 weeks and we met up with quiet a few single female travellers .

Jordan is a safe place for you to travel as a solo female. It is nothing like Egypt and Morocco. Any option will be safe. A backpacker bus from your hotel/hostel sharing with other travellers, Local bus or hiring your own taxi/driver. Met solo females who did all of these who had no issues, only helpful people making sure they were Okay and going in the right direction.

I would do a day trip out to Jerash also. And if you have time a dip in the Dead Sea.

Only sight see in Amman for 1 day, the sights are better outside the capital.

Have fun

When are you heading to Jordan? I'm also a solo woman and will be there June 5 until 11 probably :)