I believe you're dreaming if you think you can get a handheld GPS to use on a bike that can do all that.
My Whistler Galileo 100 which can be bought with the mapping software for less than $100 these days can probably do 70% of what you listed.
It has North America base maps built in, comes with a 32 meg compact flash memory card for downloading detailed maps. The map software is so accurate it's scary...there are streets on it for neighborhoods in my area that are still under construction, technically some of the streets didn't even exist yet when I bought it.
I can search exact locations, it has an unbelievable amount of POI's that you can search within so many miles.
For example I can do a restaurant (or gas station, hospital, hotel whatever) search within 5 miles and it'll show the location and even give me the establishments phone number. If I pull into a BurgerKing parking lot it'll show "BurgerKing" on the screen.
It's got all the basics like zooming from .2 to 200 miles, breadcrumb tracking, current speed, average speed, compass, altitude, time (military only).
It'll store 20 routes with up to 30 waypoint each.
It will also store 5 Track Logs (bread crumbs) with each track recording up to 2,500 points.
With the push of a button I can have the screen display in horizontal or vertical mode.
The display also has an indigo blue type of backlight that can be programmed to stay on for a certain amount of time to conserve batteries or indefinitely which is nice if you're using the vehicles power.
I can have North as always up or have the screen image automatically rotate to the direction I'm traveling which is nice since I don't have to think whether I need to turn left or right depending on Norths direction.
It takes 2AA batteries. I use rechargable NiMH batteries and they typically give me 8 to 10 hours of continuous use.
It's water proof for 30 minutes while submerged at 3 feet. Has an external antenna jack.
Everything is downloaded via USB cable.
I've had mine for several months now and love it, I've probably learned about 50% of its features.
Only complaint I have it that it doesn't record "top speed"...then again I haven't checked what it does in recording mode so I could be wrong there.
I paid $90 for mine off Ebay with the accessory upgrade pack which includes the mapping CD's, USB cable and 32 meg Flash card. Everything was brand new in the box.
I see my local Walmart has them for $100 and another $50 for the upgrade pack.
What's nice is that you can snag these off of Ebay really cheap since the world is full of lemmings who only want the overpriced underfeatured Garmin series GPS to go along with their $200 Nike shoes and Progressive Insurance
Seriously if you think about it the Galileo is the same price as that bottom of the line yellow colored crappy eTrex that does absolutely NOTHING...no maps, no memory, no PC hookup, just basically gives you your coordinates and thats it.
I know the OP probably doesn't care about this particular GPS since it's not the ultimate color display top of the line unit, but hopefully the above info will help someone who wants a very inexpensive model with a ton of features.