Can you share wifi from mac (no ethernet) with iPhone over cable or bt?

I'm traveling to Canada where internet rates are ridiculous over cellular. I intend to use hotel connections. In many cases, hotels want you to pay per device. I'll be bringing a MacBook Air (no ethernet) and an iPhone. I would like to log into the hotel's wireless internet (WiFi) with my MacBook Air and then be able to use that connection with my iPhone.

I have activated AT&T personal hotspot, but I won't be using that in Canada to share a cellular connection.

I would like to be able to connect the iPhone to the MacBook Air using either Bluetooth or a regular iPhone charging cable and have the iPhone connect to internet through the computer.

This would be easy if I had ethernet in the Mac because then I could share the ethernet connection over wifi. That would require buying the Apple USB ethernet dongle. Yes, it's possible, but it won't solve the problem that arises if the hotel does not offer ethernet.

I've tried everything I can think of. I have tried to pair the iPhone with the MacBook Air over Bluetooth. I get so far, and see the six-digit code, but apparently the iPhone doesn't support the full Bluetooth personal area network (PAN) protocol unless personal hotspot is active and the iPhone is connected to cellular data (expensive in Canada) -- then it's the iPhone data that is being shared, not the computer's. I also tried plugging the iPhone directly into the computer. Again, this works only when personal hotspot is active and the iPhone is connected to cellular data.

By the way, strangely, this all works just fine with my iPad 2 running the latest iOS. I have a 3G (AT&T) iPad 2, but I have not activated any kind of cellular data on it yet. I put it in airplane mode, then turn on bluetooth. I can quite easily pair the iPad with the MacBook Air's bluetooth, and as long as the MacBook Air is connected to WiFi, the iPad has a little picture of two rings (linked) next to the airplane mode symbol. All internet functions (surfing, e-mail, internet-enabled apps) all work just fine.

Why does this work so well on the iPad and not at all on the iPhone? It's very annoying.

While I started out settling for having the computer be the main paid hotel-connected device, I would also be OK if I could connect the iPhone to the internet and have it supply connection to the MacBook Air. However, I cannot seem to get the iPhone to share an active wifi connection with the MacBook Air over bluetooth or cable in that direction either.

So are my only options to get an ethernet dongle (if the hotel has ethernet) or a usb wifi stick (if the hotel has wifi)? Neither of these is a particularly appealing option. I can do almost everything from the computer that I would do with the iPhone, but I have many apps set up on the iPhone that are more efficient and enjoyable to use for some tasks.

Thanks in advance for any advice.