I really wish you well. It is tremendously hard to apply for a job these days.
Used to be you walked into HR (Personnel) and filled out a paper application, got to have an interview on the spot with the hiring Nurse Manager (Head Nurse of the particular area you wanted to work in). LOL
Now HR holds all the power. Usually, you must fill out your app online and do that from home or a public computer if you don't have a home one. HR will then tell you, if you call to follow up a few days later, that they don't have the time or manpower to check the status of your app, they will call you if you are needed, and basically you should go take a hike.
One HR person actually admitted that she holds app back when she gets "too many" for any position! She will give to the hiring Nurse Manager only those applications falling inside a certain time frame- like, for instance, the ones received in November 1 - 15, (and containing the magic words chosen for this particular position).
Maybe other people don't find the process overwhelming, daunting, and fraught with so much ^(**+=_(&@@#$% that they are tempted to just go fishing. I hope you have a nice easy time of it and get to work in your dream area.
As far as writing a letter, just call the ward and ask for the name of the Nurse Manager and then write away!