Fluorescent Without Fixture
Q:  Is this possible?  How could I do it?

A:  Certainly possible, but there are some obvious issues:


The open circuit voltage for T8 instant start ballasts is up to 600v.
Most ballasts require installation on a metal enclosure for heat dissipation and RF shielding.
Most ballasts require fairly short wire separation distances between the ballast and the lamp (perhaps 6'-- some specialty sign ballasts will go longer distances).  
Most T8 fluorescent lamps supplied by an electronic ballast are electrically very noisy.  Moving the lamp away from a grounded metal enclosure makes noise containment worse.  In a residential environment, one might be very unhappy with the RF interference.


Have you considered an LED lookalike for the T8 fluorescent?  There are units available that run directly on 120v line voltage. The initial lamp cost on these is high, but if you are building a custom piece of light fixture art, that may not be an issue.  One example is model 1920WH-L (I am not endorsing this particular unit):