It is not an especially satisfying or educational build project, and it requires you to buy some proprietary hardware and software. I submit this for people who just want something that works well.
Step 1: Select a Bullhorn
The most important feature for ease of building is that it has a detachable microphone input jack. This is typically a 3.5mm mono plug as seen in this photo. You can find many of these on ebay by searching on the term "bullhorn".
15 watts is a good level for polite social interaction in a noisy bar, go at least 25 watts if you want something that's louder than you can yell.
Step 2: Portable Text to Speech Device
In the end I found a Treo 700w mobile phone that someone was replacing with an iPhone. It runs Windows Mobile version 5.0, has a handy touch screen, and the battery lasts a long time. The phone and wifi features can be turned off so that it is just like a PDA.
Install Cepstral software on the phone. You can buy different TTS voices for around $20 from http://cepstral.com/ , demo them first to find one you like. Seriously, I tried a few other software options and feel this one is worth the extra cash. Unlike others I tried, the voice sounds good, it runs very fast, and has visual feedback in case you want to give the bullhorn to a deaf friend :)
Step 3: Connection
Generally the PDA will use a 2.5mm headset jack. You can buy a 2.5mm male to 3.5mm female adapter at Radio Shack, then complete the connection with a 3.5mm male to male cord. It should not matter if you use stereo cables instead of mono.
You could also take the end of the 3.5mm mono cord from the microphone that came with the bullhorn and solder it to the jack from a cellphone headset.
Step 4: Next Steps
Disable the siren button. It's dangerous.
Add a sound activated LED for visual feedback when it's working.
Use the same principal to connect to a walkie talkie or cell phone.
Get a bigger bullhorn, much bigger.
Use a speech to text software to translate in the other direction.
Let me know in comments if you have more ideas!