I don't think there is a column for network contribution in the business transaction dashlet but what you can do to get an idea of the network contribution is use the transaction flow dashlet.
Once you open the transaction flow, right click on the title and select edit filter. Then you will go to the business transaction tab and add the business transaction that you are interested in. Once added your transaction flow will only show the teirs and contribution percentages for the teirs involved in fulfilling the transactions related to your BT. Finally, at the top click "show" next to Inter Tier Time Per Transaction which is simply the time the packets spent in transition on the network. Note: you may need to zoom in to see the inter tier times once you turn this selection on.
Not sure if this applies here but if you have UEM then there is a measure for the network latency of page actions which will work for user action or visit based business transactions. This will be measuring latency from the client perspective if that is what you're looking for, otherwise David's solution is the preferred one: