Visually summarizing phylogenetic networks
Firstly you treat this as two separate independent calculations.


The traditional approach is simply to produce a consensus phylogeny using your Bayesian method and assess the equivocal bootstraps/Bayesian probability.
Feed your data set (not the trees) into NeighborNet within SplitsTrees. There are statistics that classify the level of departure from a bifurcating phylogeny.


Examine both outputs for orthogonal support for incongruence.

Note Phylogenetic network statistics are a relatively soft area of phylogeny (they are not used as hard evidence).

Networks from Bayesian trees

The final approach (which is what you are asking about), is to feed your Bayesian trees into Dendroscope, this is a GUI that represents the uncertainty between different bifurcating phylogenies as networks and you can use it to understand the incongruence between different trees within your Bayesian MCMC, because the phylogenetic networks directly corresponds to the level of incongruence.

Dendroscope is a nice Java API and is very easy to use.