The DC bias conditions will remain the same. For eg., for a voltage divider bias, i use collector resistance Rc=10k, emitter resistance Re=1k and voltage divider resistances as 361k and 33k.
For a colpitt's oscillator, in order for the system to break into oscillation, there is a constraint on the AC voltage gain.
Av > C2/C1
where C1 and C2 are capacitors in colpitt's feedback network.
So, initially, determine, L,C1 and C2 for the required frequency,
Then find the minimum value of gain (C2/C1).
Choose your gain to be higher than this ratio, and say your required gain turns out to be some 20, then use 500 ohm and 500 ohm series combination for emitter resistance,
and bypass the bottom 500 ohm resistance by a suitable bypass capacitor, so that your AC gain now is Rc/unbypassed Re =10k/500 =20.
Now your system will work as a oscillator.
I think this would do it.