Bullhorn bar + STI brake/shifter I'd like to install a bullhorn handlebar on my existing hybrid bike and would prefer to continue using my flatbar Shimano STI R42O gear/brake lever system rather than a bar end brake/shifter solution. I have a 2/8 gear configuration and caliper brakes.

I've been researching it for a couple of hours now and it seems as though this may not be possible. Why? Is it to do with the space required for mounting the brake/shifter? Or is it simply down to the market not providing compatible bullhorn bar and shifter ring diameters?
If you have flat bar shifters, most bullhorns have a different diameter than flat bar shifters use. But you can find bullhorns which have the same grip diameter as flat bars and clamp the shifters on (though these are comparatively rare). Then you have to make sure the ergonomics work for you.

My suggestion if you want a few more hand positions is to buy some bar ends. Ergon makes some fantastic ones, albeit a bit pricey. 

Edit: I saw STI shifters, which normally is just used for the drop bar brifters, so the remainder of the answer may be useful for that. 

The bullhorn diameter has to match (and most bullhorn bars satisfy this, though you can also get bullhorns for mountain diameter). Worst case, you can always cut a drop bar to get a bullhorn. 

The bigger problem though is that you have to shift -- the STI shift motion is pretty hard to pull off on anything other than a standard drop bar. The cable routing is a bit weird, and its not necessarily the case that you'll be able to fully use the brake lever when using STI shifters depending on how its installed (actually thats probably the biggest problem -- you don't need shifting but you do need good braking). Also, the ergonomics of a STI hood were designed for a drop bar

People have done this though and some people like it. Bar ends and aero brake levers are neater to route and likely easier to shift/brake with though.