How to update bias in CNN?
Like the update rule for bias terms in dense layers, in convolutional nets the bias gradient is calculated using the sum of derivatives of Z terms:

$$ dJ / db = \sum_h \sum_w dZ_{hw} $$

which J is the cost function, w is the width of the activation after convolution and h is the height of the activation after convolution.

db is computed by summing  dZs. It means you are summing over all the gradients of the conv output (Z) with respect to the cost.

Calculating the error of the net depends on the cost function that you have used. Depending on using cross entropy or mean-squared-error or other justified cost functions, you may have different update rule for other parameters of your net. But if you use cross entropy which is common for variants of classification tasks, the above update rule is used for updating bias terms.