What is the Capacitor and Resistor formula to delay the turn-on, saturation, of a transistor?

In general the formula you are looking for is the time constant in seconds = R C  , with R in Ohms and C in Farads

However this is not that precise for a transistor because a transistor is non-linear and has its own resistance which varies.  

Give it a try.

A capacitor in series with the base of a transistor will not work.  Keep in mind that a BJT requires current flow from the base to the emitter in order to turn "on."  The capacitor in series with the base will block any DC current so at most the capacitor will discharge through the base and that's it.  

Once it has discharged, it cannot be recharged because no current can flow into the side of the capacitor facing the transistor.  Of course, no current can flow from the collector to the base and no current can flow from the emitter to the base because this acts like a reverse polarized diode.

What I think you meant to do was connect the resistor and capacitor in series and attach the base of the BJT between them.    The other end of the resistor and the collector are connected to power, the other terminal of the capacitor is connected to ground, and the emitter of the transistor is connected, through your load, to ground.  This will slow the start up of your load but not really delay it.  That is the current to your load will increase slowly when you apply power to your circuit, but it will begin to flow almost immediately.

If the capacitor is connected to the base and, say ground, then yes, it will delay the saturation of the transistor.  Capacitors don't pass DC current, so a true series connection won't work.

The resistor value will be determined by the base current needed to maintain saturation.  Knowing the resistor, final voltage to the base, base trip voltage, and the needed delay time, use the following :

C = T / [ R * ln( Vb / Vtrip ) ]