My goal is to be able to use an app on my iPhone(made by me) to execute commands on my RPi. I know Swift fairly well, though I am not all that familiar with using Bluetooth and Swift(though I am confident that I can figure this out). Would this be possible? Could I connect to my RPi from Bluetooth, and then could I actually execute a terminal command?
Of course it's possible. You'll need an application on the RPi that monitors a Bluetooth dongle for traffic, and then execute commands based on what it receives from your phone.
How that's implemented is up to you.
Since the raspberry pi uses a version of Linux, I would write a script checking for incoming Bluetooth connections. Once you pair phone and raspberry pi, you will be sending data over the link. Also, consider whether Bluetooth is the best protocol. WiFi is higher performing speed wise, according to a brief Google search, so if you are, say, doing any high fidelity streaming or gaming, use WiFi.