I have had similar difficulties. There seem to be (at least) three problems.
(1) The connection sequence is very counter intuitive. It goes like this: on the iOS device, switch on the Personal Hotspot. Make the Reach device discoverable. On the iOS device, wait for the Reach to appear, click on it and pair (so you pair from the iOS device, NOT from the Reach). Once that’s done, go back to the Reach and switch to the WiFi tab. The iOS device appears as a WiFi network(!!!) and you can connect to it using the WiFi password, which is displayed in your iOS device in the hotspot menu. Sometimes you need to switch Bluetooth off and on at both ends and switch the iOS hotspot off and on to get the two devices to see each other.
(2) Once paired, there is a hidden rule for connecting. The Reach will not connect to an iOS device unless something else is already connected! Fortunately I have an iPhone and an iPad, so I can log into the iPad with the iPhone, and the Reach will connect to the iPad.
There is another more sensible rule that if there is a usable WiFi network available when the Reach is switched in, it will use that rather than a Bluetooth connection. This means that if you are at home, it will use your home network.
The initial configuration stage is very tricky. Initially the Reach connects to your home WiFi or, if that’s out of range, it creates its own WiFi network. If I connect my iPad to that, it breaks the connection from the phone, so that’s no longer logged in, and the Reach will not connect to the iPad. So I need a fourth device such as a laptop to connect to the Reach while the phone is connected to the iPad. I can then set up and configure the WiFi connection to the iPad and then instruct the Reach to switch over to it.
Usually, if you have all this configured AND there is no WiFi network available AND the iPhone is logged into the iPad, then when I switch on the Reach, it connects automatically to the iPad and uses its Internet connection, so I only need those three devices. Usually. Occasionally it doesn’t, and I have to connect to the Reach using the fourth device and persuade it to connect to the iPad all over again.
So now when I go out into the field I have to carry an iPad to provide an Internet connection, an iPhone to allow the Reach to connect and a laptop, in case the whole ramshackle arrangement decides not to work today and I have to kick it all off again.
None of this is documented in the manual, which is why everybody who has an iPhone finds it impossible to connect.
(3) An iOS device can’t always see a Reach over Bluetooth. I have two Reach M+ devices, bought at the same time. Initially they were running the same firmware. The iOs device can pair with one of them, but not the other. The second Reach doesn’t appear in the list of devices that it can pair with. I’ve messed about switching bluetooth off and on again. I just upgraded the Reach firmware to the latest version but that did not fix the problem.