Has construction on the house started?

Yes, the house is 20 years old but the basement has never been finished.

Not enough information, need more dimensions, i.e exact window/door locations from corners and sizes and height off the floor, extract stair location and dimensions, column exact locations and dimensions between and from walls, etc.

The bedroom requires emergency escape egress, so the planning must take that into account. The window size, and the ground level outside the window, are of primary importance.

As DeWayne pointed out the bedroom will require emergency egress. If the bedroom can be on the walk-out side of your home that doesn't present a problem. If the bedroom is below grade you will have to install a window, a window well and a ladder to get up to grade.

I feel like a broken record, but find a local residential architect that can gather the pertinent information required to finish the basement. A lot more information is needed to do what you ask. If I had a project like this, I would want to know the layout of the spaces above, window sizes, column/beam locations, duct paths, joist direction, height to underside of joists, your budget, why you want to finish the basement, and a myriad of other bits of information.

We had the same issue with the sump pump location. Built a box over it with full access by lifting up the lid. It's in front of the egress window and serves as a step into the window if need be. Good luck with your project!

It looks like there is a door to the patio, so that’s egress from that level. Whether or not you want to use a bonus room as a bedroom is up to you.