OK, I thought the speaker directly had two pads like the charger? Wasn't clear, now it is. The speaker has an USB connector for charging, then your solution shown on the diagram will work. Yes, you can use a simple diode bridge - use Schottky diodes and make sure they can handle the charging current. You'll get a voltage drop, then whether it's still within specs for the charging circuit inside the speaker - you'd have to test that.
There are ideal full bridge controllers, such as the LT4320, but they usually require 4 external mosfets, besides, this one isn't for voltages under 9V, so that wouldn't work here. I haven't looked up thoroughly, so if someone has found something that can work at 5V and ideally without the need for external transistors, I'd be interested in seeing that myself. You could also use so-called "ideal diodes" (eg:
http://www.ti.com/product/LM66100 ), but you'd need 4 of them? No big deal but unless you know for sure you can't charge your device with a full bridge made of Schottky diodes, I'm not sure this is worth it.
As mentioned above, a QI adapter would also be a solution and more elegant. Then I wouldn't bother keeping the charging dock. Just buy a QI-USB adapter (you can find them for a few bucks, look up "qi usb adapter") and a QI charging dock (can be found around $15, maybe less).