I have never stepped foot in a gym.

I work out from home as well. I started with the same equpiment you have, except the bike. As time went on and I progressed, I slowly added things. I could not live without my adjustable bench, it has a rack to put a barbell on (for barbell chest presses, incline presses, etc)...which I also use as a squat rack...lol And, it has a preacher curl platform and at the foot it has the necessary attachment to do leg extensions and leg curls. It cost about $60 at walmart and it is the one piece of large equipment I would advise you to get. I would also advise:
Barbell and some weight plates
Adjustable dumbbells...like barbells, but dumbbells and you can use the same plates for both.
I can't answer your question about bikes as I don't have one yet but I am looking into one so I will be interested in what people say.
As for back exercises....I now have a home gym which was only $150 and still in the box...lol but I do bent over rows with barbells and dumbbells. You could also buy a chinup bar that you put right in your door. Mine came with two sets of anchors and you can move the bar to either. I have one set high for pullups and one set low for reverse pushups...both work your back really well. It cost $20.
I hope that helps a little. I am sure others have really great ideas as well. I am here to tell you that you do not need to go to a gym to workout. Over time you will accumulate more things. I find doing it in small steps hurts the purse the least.