If you are sending from Australia to the US here's a quick guide:
Your postal service will have rates to the US online so you can look them up. A typical fan mail request coming back to you from the US will cost $1.10. You can use US postage stamps on your SASE (several members here sell them) or include a few single $1 bills.
If you want an exact cost then use
www.xe.com/ucc to get from US$ to AU$ and add on the cost of Australian postage and your photo if you choose to send (I order from the UK Snapfish and usually shop with their many offered discount codes and pay as little as 5p per photo, sometimes free shipping too!)
I don't think sending a photo with your letter and SASE will push the price up to the next band, $1.10 covers up to 1oz in the US and I believe Australia has generous Airmail pricing bands.
For Bruno Mars, look at his info page here and read some of the feedback to see what people are getting back and where from to decide if there is more than one address supplied.