According to Eventide Tech Note #200:
MIDI control of the Bypass button is not supported on the H3000.
However, here are two suggestions that might be helpful:

You can create a blank program with nothing but input and output. This program location will become your bypass.  You will have to set the input and output level.  This is what some users do and it works great, and there is no coloration of the sound.
If the H3000 is run in parallel within an audio system, not in series (like in a guitar amp FX loop), you could use CC#7 and control the H3000 output level. This will mute the unit when desired.

Its interesting that the old manual says there IS a relay bypass CC destination at CC#8196 (14-bit CC) data: 0=bypassed; 1=active
If you want to put this to the test:

(1) Set up a MIDI sequencer: Install a sequencer program like MidiOX/SySexy on your laptop and hook the MIDI interface i/o to the 3000 i/o
(2) Configure H3000 for sequencing:
FUNCTION 3 times, then select “Expert”, then SysX= ON
FUNCTION 5 times, then select “ENABLES”: Seq= ON Lvls= ON Rcv= ON
(3) turn on the sequencer program on your laptop, then press the BYPASS on/off while sequencing, watch your sequencer for the output.
(4) Try re-sending the Bypass ON and Bypass OFF messages back to the H3000 thru the sequencer, if they appeared, and see if it works by sending MIDI.