New window in walk-out basement wall
Before you go to all the trouble, find out if the new bedroom needs a egress window that has different dimensions and specific requirements for the height of the bottom of the clear window opening. These may not be required now for your aerea, but in many ways, they are not "grandfathered" since are safety and occupancy item, not like building code requirements.
It is good to think ahead since when you go to sell a buyer home inspector might catch a non-conforming window or worse yet, the areas could be classified as not a part of the living area and the amount of money for financing could eliminate many buyers unless they have a good cash downpayment.
Just a heads-up for consideration, even though you say the basement is a walk-out (I assume this is acessesible through the walk out to serve the entire basement area, but you never know).