Does this look like a correct Bandpass filter?
The ratio of centre frequency to bandwidth is called Q and Q, for a series resonant circuit, is also dictated by R, L and C using this formula: -

$$Q = \dfrac{1}{R}\sqrt{\dfrac{L}{C}}$$

Plugging in your circuit values I get a Q of 413. If I considered the centre-frequency to bandwidth ratio, I get 65.75 so, it looks like you will be "sharper" in resonance than your specification demands and this can cause problems.


  I need to know if the method (using the equations I listed) is the correct way to determine my RLC values


The ratio of R to L does give you the bandwidth but that bandwidth is in radians per second; you have assumed it is in hertz hence, the value of Q of 413 (gleaned from my formula and your values) is precisely \$2\pi\$ times higher than 65.7 (\$f_0\$ to bandwidth ratio) and that is your only mistake. The formula for resonant frequency is correct.