How do I use a data set with continuous variables with the BayesNet classes?

Use the class weka.filters.unsupervised.attribute.Discretize to discretize them. From the command line, you can use
java weka.filters.unsupervised.attribute.Discretize -B 3 -i infile.arff -o outfile.arff
where the -B option determines the cardinality of the discretized variables.