Since the zip code you have listed is within the City of Chicago I will assume this question pertains to a property within the City limits.
A bedroom does not require a dedicated egress path to the exterior. Granted you have to be able to get out of the bedroom. Presumably the same way you came in. However, it does not need a direct path to the exterior of the apartment or structure.
8% light / 4% ventilation ARE required for a compliant bedroom. Whether that requirement is met either through the use of a window or other means is another matter. A window is obviously the most common source. However, borrowed light and mechanical ventilation are acceptable alternatives under the Code.
Since you are creating this bedroom, i.e. rehab/new construction/alterations to an existing structure you will also have to meet other requirements such as minimum size, heating and electrical.
You can have a compliant bedroom in a basement in the City and in the burbs. There are various requirements of course that need to be met. In the burbs basement bedroom requirements tend to be stricter.
There will be variations on the requirements based on what type of building you are in. Single family, highrise, etc.