I am pretty sure (from a google search) that the answer is no, but worth asking.

I use the Strava app for my iPhone. I am NOT interested in putting the phone on the bike, as I keep it in the back pocket where it belongs.

I was recently given a Pebble watch as a gift, and I really like that it is an extension of my phone display. I can easily see who is calling or texting me while the phone stays put.

I don't see an iOs app for Strava. Bummer, as it would be kinda cool to see what's happening with my ride, in real time, on the Pebble watch.

Any suggestions??

I'm assuming that you are asking if there is a version of the Strava app that will display your ride metrics on your Pebble? If the Pebble is not listed in the supported devices section of the app or on their web site, you are correct in saying the answer is NO. While it does nothing for your Pebble, it does support Apple Watch.

Yes that's what I am asking. I am actually surprised Strava does not support Pebble, it seems like a good match. Maybe some day.

I think if they become more popular, there is a chance that it will be supported by some of the available cycling apps. At one point, the FitBit was not supported and now a few do interact with some of the FitBit models.

I have never used this app, so don't take this as an endorsement in any way, but it does reportedly have Pebble support:

World Champ Tech - Apps

This is the first time I've heard of this app. If the OP isn't using any speed/cadence or heart rate monitors connected to his phone, this may just be the way for him to go. Looking at the web page and the screen shots, it doesn't look as if it is compatible with BlueTooth sensors.