Kari, Susanne's book is the only biography of Murdoch that was published (the best by default?). The first version of the book was Good-Bye, Good Luck; and as Henry said, it was a limited edition, long out of print and very hard to find.
Her revised and expanded version of that book is the one Jesse mentioned. This is actually the better of the two to get as it is greatly expanded from the original version. It has a tremendous amount of research into his career in his earlier years.
Unfortunately, that book also appears to be out of print, and I tried and could not pull up Susanne's website either. I did a quick used book search and could not find any copies for sale.
Giving all that, you may want to turn to the net. His home town of Dalbeattie has a nice piece on him. Here is the link:
http://www.dalbeattie.com/titanic/wmmlife.htm
all the best, Michael (TheManInBlack) T
p.s. Actually there was another bio written by Elizabeth Gibbons, but it was, to my knowledge, never published (although part of the book was printed in the THS Commutator a few years ago).