Is it possible to connect the center tap to the negative of the first filter cap and use a bridge rectifier ...
The negative of the first filter cap
is ground, so making that connection shorts half the diodes of the bridge.
EXCEPTION:
If you have series filter caps for a higher total voltage rating, you could connect the center-tap to the junction of the two filter caps (mid-way between B+ and ground).
Is it possible to connect the center tap to the negative of the first filter cap and use a bridge rectifier and not double supply voltage?
Not like you're thinking.
"Double compared to what?" This is the question you should be asking yourself.
A fullwave rectifier is normally used with a center-tapped power transformer. The CT gets grounded. When the transformer is energized, one end of the total secondary winding is positive compared to the CT, and the other end is negative compared to the CT. For our B+, the end with the positive voltage compared to the CT forward-biases the diode it is connected to and passes current. The other diode is reverse-biased and blocks current.
*At that moment, the diode which is conducting allows a voltage to appear at the first filter cap which is equal to the voltage at that end of the transformer winding through to the center-tap.During the other half-cycle of the wall voltage, the voltages of the ends of the secondary winding reverse, and the opposite diode conducts again with the same voltage appearing at the filter cap.
*The important thing to see is that a full-wave rectifier and center-tapped transformer winding is connected such that the filter cap only sees the voltage of half of the total secondary winding at any moment. So a 300-0-300v PT only presents the positive half of 300vac to the first filter cap, and the cap charges to the peak voltage of 424v, minus diode voltage drop.
Bridge rectifiers don't use a center-tap (except, as PRR pointed out before, when you're building a bi-polar supply; but that doesn't apply to vacuum tubes generally). The arrangement of diodes is such that at all times there is a direct connection between both ends of the transformer secondary to the first filter cap.
For the same 300-0-300v winding described earlier, the filter cap sees 300+300= 600vac, rectified and tries to charge to the peak voltage of 848v minus diode drops.
*As a result, transformers intended for use with bridge rectifiers are wound for half the total voltage from end to end of the secondary.So "doubling" of voltage when using a bridge with a transformer intended to be used with a full-wave rectifier is only a comparison of what voltage you get in relation to what voltage you expected. And the doubling is only due to utilizing the entire secondary all the time.
Is it possible to connect the center tap to the negative of the first filter cap and use a bridge rectifier and not double supply voltage?
To answer your question after presenting all that... The way to not double supply voltage is to use the full-wave rectifier as intended with the transformer in question.