Can I put bullhorn bars on a bike with hydraulic disc brakes The most comfortable bike I've ever owned was a road bike with bullhorn (aka pursuit) bars. I actually had a pair of STI levers on it, mounted upside down (with the handles pointing forward). They looked kinda scary, but they were really good that way - I found it was much easier to use the levers that way than on normal road bars.

I've since moved on to a flat-bar road bike with hydraulic disc brakes. So my question is - is there any way of getting bullhorn bars going with the current setup - ie hydraulic levers and mountain bike style gear changers. I could conceivably turn the brake levers upside down again and then get bar end shifters for the gears. Would that work?

Or is there an off-the-shelf solution?
Your options are fairly limited, nearly all bullhorn bars are sized for 23.8mm road brake levers, while mountain levers are sized for 22.2mm handlebars.  There do appear to be some 22.2mm bullhorn bars listed on eBay currently, but your mileage may vary.

You may also have luck finding some 22.2mm "north road" style bars that you can flip over or trekking bars with close to the right shape that you can cut down. Alternatively, a set of hydraulic brakes with suitably modifiable clamps.

As far as better levers than just using your mountain levers, it's expected that drop-bar hydraulic levers are coming in the not-too-distant future due to disc brakes' recent legalization in UCI cyclocross.  In the interim there are some pretty ugly hacks, basically involving running a set of cables from a cabled brake to an interim hydraulic lever. It's not elegant, to say the least.