You didn't indicate a home or what you want to do about it. First, be very careful about rentals you find here and anywhere online. There are so many scams it's dangerous. DO NOT send money or complete an application until you view a property IN PERSON with the owner or a license agent.
The best place where you will be able to find something like this is going to be on Westside Rentals and Craigslist.
From experience, you may have a challenging time finding a 1 bedroom for $900 in mid Wilshire.
Have you thought about looking in the Valley? The commute would be about 30 minutes but you would be able to a get a little more for what you are looking to spend.
Let me know if you would like a list of buildings that may be able to accommodate your budget and needs.
Prime Partners @ Keller Williams Realty
818.859.9930 - Direct