Is the total shape of a bell curve greater than 1?

It is assumed that by "shape" you mean "area".

The quick answer is yes, probably. The "Bell curve" is called a Gaussian function (see related link). The area under a Gaussian is not necessarily 1; it can be anything.

However, if you're talking about probability, where the probability distribution is in the same of a Gaussian, then the area under the curve must be exactly 1. This isn't however, because it is a bell curve, but because it's a probability distribution.

The area under any probability distribution must always be exactly 1, or it isn't a valid distribution.

The proper term for the total area under any curve f(x) is the integral from negative infinity to infinity of f(x) dx