Plectron. I'm a motorcycle rider and my wife and I use the Garmin 376C & 478. Both of these are advertised as "marine" units, but they actually accept street maps just fine and they do an awesome job monitoring the weather radar with the use of Garmin's GXM-30 antenna. It has saved us many times when on week long trips. One time we were riding south through the midwest while Hurricane Gustav was heading north from TX.
Its helped us many times adjust our route to avoid the worst of storms or just take a short break to allow a small cell to pass. I impressed several guys one time when a group of 13 of us were going along and I stopped everyone on a small backroad for about 15-20mins as I saw a strong cell just ahead of us. We sat around talking for 20mins and could hear the thunder in the distance. We never got wet where we sat and once we wen through the area, the rain had move out, but the roads were still wet. Everyone was so impressed. Most times it works pretty good.
Now, although these units aren't exactly hand held (though they are portable), they have a really nice screen size & color, they are more then capable to be mounted on a handle bar with the RAM mounting system or something else. I have my XM antenna mounted on a metal plate right behind my unit so it stays attached to the GPS unit. My only concern in your application would be battery life. While the GPS unit itself can run all day off battery power without the XM antenna hooked up, with the antenna, it brings the battery life down to about 3 hrs. On the MC, we just run off our battery power, but this may be much more difficult on a bicycle.
There's also going to be a pretty significant upfront expense buying the GPS unit and XM antenna, but over the long haul they pay off. The GPS unit obviously requires no subscription and you can turn on/off the weather subscription as you need it. I just turn mine to "end of season" when I don't need it or just down to one of their really cheap monthly overview packages.
As for GPS's that do this, the series I'm showing you here are part of what we call the x76/x78 series. 276c, 376c, 378, 478. All 4 units are identical in appearance, just the software in them differs. The 276c doesn't accept the XM antenna, so its out. The 376c requires Garmin's proprietary memory card (largest 512mb) to hold maps. It accepts the XM antenna and broadcasts XM music and can do full weather below. The 478 is identical operation wise to the 376c, but holds the entire US on internal memory and still has the memory slot for more/additional maps. The 378 was sold as in inland lake GPS, but Garmin screwed up and made the map set unique in that the map set with the lake data was unique to this unit. In the MC world, this made it a pain when doing routes, because it always tries to re-calc what you draw on the PC and I think updating the maps might be a PITA. You don't see much of these out there. So the 376c/478 are your best bet. All of these are discontinued, so you have to find them used.
The latest GPS they came out with to replace these are the Zumo 660. I believe it even has an update GXM-40 antenna. I haven't seen one of these in action yet though?
There are some other Garmin GPS that do general "Nav Weather", but this is more just an overview and is not up to date nexrad like I show you below.
Here's some posts from an MC forum where I was showing what the 478 can do and show.
Here you go. With the $50 package as I was saying, you get storm cell notifications and lightning strikes and a few other things I can't remember right now.
This was a storm my wife and I were dodging recently out in CO. This particular cell was moving NE but was blowing up quite radically and we were trying to get by it and head East. You can see the lightning bolt that hit right in front of us.
Here's a storm cell projection. The more boxes it has, the larger and faster it's moving.
It got downgraded here a bit
When you click on the storm cell, you get info like this on how tall the ceilings are, any hail associated with it, how powerful it is (dbz), and direction of travel and speed.
This was just a mess. We actually managed to stay relatively out of the worst stuff
You can see this one has two different cells that are blowing up.
Thats ugly!
We actually veered off here trying to miss the red stuff.