Why do you think "not having" Bluetooth is a problem?

A few years ago at work, they had a walking contest, winner gets money. So they gave everybody a device called a Fitbit to measure how far we walked. Its data is only available over Bluetooth. This was before everybody had a smartphone, so it came with a little "dongle" that you plug into the USB port in your computer - a Bluetooth receiver. If this was in your computer, the Fitbit would sync your data through your computer to a server on the internet. I know you have a computer. I don't know if you have a phone. I don't know how widely available those dongles are or if they're specific to the Fitbit or what. But there are cheap solutions that make BT a viable option. (Hell, I have a few of those dongles collecting dust on a shelf and I'll mail you one for free if you want it.)

Why do you want a watch? For this I mean. Supposing you could get a tablet (like an Amazon Kindle) and a Bluetooth chest strap, for much less than your budget, would that be acceptable? A lot of people set up a stand or handlebar mount with a phone or tablet and find it more convenient than looking at their wrist. Also unless your vision is stellar you'll probably appreciate the bigger screen. You're asking about a trainer, so everything will be stationary.

I'm not trying to talk you out of a watch, in fact I love having one. I'm trying to get you to share your reasoning. It's an exercise to help narrow it down to what you want.