The bass amp will work fine, and will give a much more appropriate response for piano than the Blues jr will.
That said, the reason why there aren’t that many “keyboard amps” out there is that the response/power needs for a keyboard are really similar to what you would need for a PA, and so most players out there are using PA speakers/amps in their keyboard rigs.
Something like this, either just one or two for stereo sound (the mono/stereo debate is the star trek/star wars-esque feud of the keyboard player’s word).
Things to note about that speaker:
[ul]
[li]It is 2-way. So, there is a driver for low frequencies and a driver for high frequencies. This, most simply, allows for crisp and clear response across the spectrum.[/li][li]It uses a 12" speaker for the low end. In my opinion this is the largest driver that any keyboard player needs. Something like this mackie 10" speaker is going to be good as well. For me, the lighter-weight 10" driver cabinets give plenty of response, sound good, and are easier to move/lift, and fit in more tight spaces.[/ul][/li]
I mentioned above that your GK would be fine. It is (and the first solution you should always try is the one you don’t have to pay extra for), but it is not “bi-amped”. So, while it’s designed to replicate a frequency range that’s closer to a piano than the Blues jr, it’s likely going to give you a kind of dulled and muddy mid/high range.
In fact, some companies who want to give bass players higher fidelity at higher ranges than is achievable through traditional bass amp design manufacture bi-amped, or tri-amped bass cabinets. And, I know many keyboard players (myself included) who use these full-range bass cabs for their keyboard rigs. Of course, as you might expect, these amps are going to be more expensive than their single-driver counterparts.
Also, I should add that I have a student who uses the same Privia you do, and I suggested he get this Behringer floor wedge. It’s quite cheap, sounds great at room volume, fits easily under/next to the piano, points the sound up to where you’d be sitting, and really makes the piano sound much better than it does through its internal speakers alone.
I don’t know that I’d try to use that to send sound out to the audience in a gig with a drummer, but in general it’s a cheap/simple/effective solution that can work in the home and on stage (provided it’s the right kind of gig).
Anyway, those are my initial scattered thoughts. Let me know if you want more (or just more concise) advice 