While it is true that mass merchandised BSO's are a pain to deal with (for bike shop mechanics) and are usually heavier than desirable, lots of people manage to get many miles out of them. You just have a much better chance of getting a bike that works really well and will last a long time when you buy a good bike with better components. You can learn the basics of bike mechanics from a number of websites such as Park Tool Company or the late Sheldon Brown's site Sheldon Brown-Bicycle Technical Information. That way you will know how to adjust and maintain your current bike and not be at the mercy of the local bike shop. If you learn what makes a good bike (light weight and mid to upper level components) you will be able to recognize one when you see it. It sounds like it will be a while before you could afford a decent new bike so an older used bike might be more appropriate. It is certainly possible to find a decent bike and sometimes a very good older bike for less than $100. An older bike, if treated properly by previous owners, can be a real find. A bit of maintenance and maybe new tires and brake pads and you are good to go. They show up at garage sales and second hand stores. Most everything there will be junk but if you are lucky and persistent, you might find one that is good and fits you. That may be the way to go. Don't do it until you learn more about bikes.

A couple simple ways to identify better bikes - weight - less than 30 pounds, no suspension, quick release wheels front and rear. The last thing is to get a list of components for the major manufacturers (usually Shimano and SRAM) so you can know which ones are acceptable and which to avoid. example Shimano MTB Component Hierarchy | Derailleur | Crankset : ChooseMyBicycle.com
and for SRAM SRAM Road Component Hierarchy | Derailleur | Crankset : ChooseMyBicycle.com There are hierarchies listed for road and mountain bike components. Anything mid level or above will be OK.