Long exposure timed shutter release

Though not programmable in any way, the Fujifilm USB remote release might do the job:

REMOTE RELEASE RR-80

Perfect stillness is critical for long exposure, telephoto, and
landscape photography. With this remote release, you can
prevent blurring caused by vibrations when you press the
shutter and never lose a priceless photo opportunity.

http://www.fujifilm.com/products/digital_cameras/accessories/others/

Or you might opt for a traditional threaded cable release.

Bulb mode appears to have a maximum limit of 60 minutes according to brochure:

http://www.fujifilm.com/products/digital_cameras/x/fujifilm_x_e1/pdf/index/x_e1_catalogue_01.pdf