Bike fit is in my opinion important only for comfort. Maybe others get more efficiency out of it, but I'm more interested in comfort than speed. I went in to the bike shop after every long ride and we discussed what hurt and what needed changed. I quickly picked up how to raise & lower the saddle, how to move it back & forth on the rails, how to change the angle. My handlebar actually allows some additional angle changes.
My brother paid for an expensive fitting and now he won't let anyone touch his bike lest they change something.
I'd try new tubes, maybe you have a slow leak. Ask your bike shop about your tires. When I started bicycling for transportation, my bike was 13 years old and the rubber on the tires was brittle and it poked holes in the tubes. You might need new tires. (I don't know how old your bike is.)
Is Mr. Right Bike a myth? When I started bicycling for transportation, it was a pretty decent bike but I quickly learned all the things I wanted different. Four years later, I finally bought a new bike that has (almost) everything perfect. Well, I bought the bike, but I swapped out a lot of things, like I wanted a smaller granny gear because I hate to power up hills. My advice is ride the bike you've got so you can figure out what you want.
That said, if it is uncomfortable, you won't want to ride it. But you can probably make your bike comfortable. With a Roadmaster or equivalent bike, I'd go either way depending on your budget. I loved riding the old bike and learning what I needed in a new bike. But if it's too tortuous, a new bike may be in order sooner than later.
I hate the straight handlebar that mountain bikes have. It hurts my wrists and my arms would go numb. There are lots of different types of handlebars, and they are inexpensive, although taking off the old & putting on the new is not trivial. I use a trekking bar, which is a very odd looking thing. My daughter uses one called an albatross bar. Google them to see what they look like.
I'd guess the Roadmaster came with a cheap saddle. You want to switch that out. Unfortunately saddle preference is another topic that is hotly debated and it's very individual so it will be challenging to figure out what you want. Considerations: 1) gel seats aren't as comfortable as they ought to be. The gel compresses into something that's harder than other materials. 2) A narrow saddle may fit you better than a wider one. It depends on your sit bones, not your girth. I have wider sit bones but I'm only slightly padded. (I was going to say slender but that might be overstating it.)
Good luck!
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike