You can use cURL through any device that supports it (Mac, Windows, Linux, etc) – or you can use Postman or anything else which can generate HTTP requests (various API commands specify to use POST, DELETE, PATCH, PUT, or GET).
Not making any assumptions about your comfort level with those things, but if any of them are unknowns or scary, this community can help guide you through the pieces.
There is also a command-line utility which the Bond team periodically will remind us about, which can simplify some things, especially while familiarizing yourself with the Bridge / API. This would likely only be quickly useful if you happened to be a Linux user.
Bond Bridges make child entities, or “Devices”, under themselves which are just virtual representations of RF (or IR, for those Bridges that have it) commands / signals.
Smart By Bond enabled devices are actual real-world devices, but in the API / automation world, each is exposed to the Bond app as an individual entity / “Device” (without any Bridge being the ‘parent’ or prerequisite).
Did that clarify anything or answer most of your questions?
Oh: bonus thing. Sometimes you can take the Signal endpoint, which is a bunch of hex, from one Device and basically push it onto another Device via the API (using cURL / Postman / etc).
However, not all Template Devices expose their raw Signal, so that may or may not be useful to you in the end. (When Merck says “one-click devices” in that post, he means Template devices)
The Template I showed above, for instance, has no Signal data stored when I query it with the API. 
Second bonus: since you’re an iPhone user, in addition to cURL and Postman options on computers, you could use iOS’s “Shortcuts” feature to make quick buttons to directly issue your Bond Bridge some instructions over API (while your phone is on the same network as the Bridge), without even opening the Bond app each time.
More of a learning tool or niche usage case, but worth poking at perhaps?