To do a Bachelor or Master of Nursing Science?

Which gives me a better chance of employment.
Im not keen on job hunting or waiting for employment.
I'll much rather be employed permanently and settle down.

I have a Bachelor's degree in Science with no Nursing background.

I intend to be a Certified Registered Nurse Anesthetist some where down the line, but I would not mind being a Nurse Practitioner except I hate to prescribe drugs because I wouldnt use them myself.

Does it make more sense to do the bachelor of nursing science because I have no nursing/medical background and so it would be easier?

Or will it be better to do the master of nursing since there is the option of me completing it in the same time as the Bachelor of nursing science and I will have to do it eventually if I am to specialise as a nurse.

And will it be easy for a Nurse Anesthetist to get a job?

I would vote for the Associates at the local community college if you do not want to spend the time for a Bachelor's Degree. The masters degree would assume you have completed a nursing degree or program diploma. However, there might be a program or two out there, and I noticed there is one called an accelerated program in Texas which would take you three years.