A Bell curve is essentially an inverse parabola converging to an absolute x-offset hyperbole in simplest form, assuming it is bilateral symmetric (as opposed to skewed). You will need some more inputs definitely, for instance the points defied on your example graph controls the start and end of intersecting, but how about the incline/decline slopes. Your example shows a very flat table-top-like maximum at x=600 but the slope might be much more gradual or sharper to the centre. I would suggest adding a slope or acceleration at least, or maybe adding a two-step descriptor such as an attack angle (early ascent from the base) and regress or release factor (i.e. how close to the top point do we "level out", if at all...).
Also when you say you need a formula for it, I assume you mean a parameter function f(x,p1,p2,p3,...)=p1x+p2x-...etc. whereby plotting it along an axis is possible? If so, possibly a scale factor might be useful. Have a great day!
Ryan