Can I put bullhorn bars on a bike with hydraulic disc brakes
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.