An 18 inchi diameter bag has a circumference of about 56.5 inches, e.g., 18 times pi (3.14159). That's more than enough fabric to make it around an oval of 22X12 (using slightly bigger numbers because I don't have a tapemeasure). The circumference of an ellipse can be approximated by the equation C = pi[3(A+B)-sqrt{(A+3B)(3A+B)**] where C is the circumference and A and B are the semi-radius values of the ellipse. Thus if A = 11 and B = 6, then C = pi[3(11+6)-sqrt[(11+3*6)(3*11+6)] = 54.6 < 56.5.

The bike will fit. Even if it doesn't seem that it should not....