Here's what I see as possible development:
The ship moves based on thought algorhythm...what this means is, the brain observes the bullets coming at the ship and produces a movement calculation based on bullet trajectory to avoid this, the ship moves based on the calculation of where the bullets are NOT heading. So in other words you won't be controlling the ship by the purest definition, you'll be controlling the space the ship moves to based on bullet movement...I know that's hard to picture.
Of course, there is room for bad calculation and this would of course mean making 'mistakes' which is the lynchpin in all shmups, really.
Also, the thought occurs to me that we would be able to mentally control bullet firing intensity, mentally calculate the firing rate and boost it in some areas while not in others...this might be useful for critical 'burst shots' in some areas of a shmup (you've seen Ikaruga do this so I think you know what I mean).
Also, another factor that could come into play...multi-directional targeting and movement. The human brain is capable of processing image movement from just about any direction almost immediately as long as the visual stimulus is within 90 degress of the human's field of vision.
This means we would be able to intercept homing missiles, dodge multi-reflected lasers (no matter how complex the pattern as we have a natural anticipatory reflex for trajectory) and even anticipate the opening spots inside complex and narrow corridors so that navigating will be a breeze.
Lastly, as possibly a safety measure...use a sort of 'instant shield' ability that only takes up a little more 2/3rds the ship's size that would be triggered to go off every time we blink...the shield itself would be able to determine reflex blink from manually controlled blink (autonomic versus mental control they DO have seperate signals you know), so that as a mini protection against making mistakes like blinking at the wrong time would actually be beneficial as opposed to bothersome.
As for bombs...I think a power guage based on our mood/stress levels would be in order...the more stress we're under from the bullet stimulus the higher the guage...when full, it fires automatically based on low stress or high stress response.
Low stress would produce a big laser cannon ala Dodonpachi.
High stress would produce a screen-clearing mega bomb that lasted for a few seconds while also wiping bullets from the screen.
The "power guage" could be calibrated to a person's natural reactions to stress as it varies from person to person...also the game will calculate your stress levels based on pulse rate when exposed to overwhelming stimuli...so no "bomb cheating" would be possible.

The world would be a better place if there were less shooters and more dot-eaters.
Jesus' BE ATTITUDE FOR GAINS:
1. Pure, Mournful, Humble Heart
2. Merciful Peacemaker
3. Suffer for Righteous Desire