Pro will show you the list of basemaps that are configured in the organization/portal you're logged in to. Ask your org administrator to add the Bing basemaps to your org, and you should see them as an option in Pro.
I actually am the org administrator. I thought I had added the Bing key, as I am able to access Bing basemaps once I "share" a map as a webmap. I just cannot get Bing basemaps to show as an option from within ArcGIS Pro. Could you point me to where I would add Bing maps to our Org so that they will show up in our portal in ArcGIS Pro?
Jeremy, we are having the same issue, we can see it using ArcGIS online maps and through ArcMap v10.3, but can not see it using ArcGIS Pro. The key has always been in our org for Bing. Where do you add the bing basemap in ArcGIS Pro?
We figured it out, though it seemed like kind of a round-about way to do so. What we did was logged into our org portal. Then we created and saved 3 blank webmaps to our ArcGIS Online account. One with Bing Maps as basemap, one with Bing Aerials, and one with Bing Hybrid. Once the 3 webmaps were saved, we shared them to the "Bing" Group that we had created in order to get Bing basemaps to work through ArcGIS Online. Once we did that, those 3 maps showed up as basemap options in ArcGIS Pro. Hope this helps...