Shaw said he would consult National before he took recommendations on the bill to cabinet in August and before the bill was drafted.
"It is a horrendously complicated issue and it is going to take a few rounds of conversation before we settle on final decisions.
"I think it is pretty unreasonable to ask them to support a piece of legislation that they haven't seen yet and I think that engaging them in the process of drafting increases the chances that they will eventually vote for it.
Bridges, a former Associate Climate Change Minister, sent a letter to Shaw and Prime Minister Jacinda Ardern, about the bipartisan approach but in a speech he elaborated on five principles that should guide the country's transition to a low carbon economy and before agriculture was brought into the Emissions Trading Scheme.
Bridges said that among the principles was having a science-based approach, which would treat the short-lived methane differently to the long-lived carbon dioxide.
That is one of the issues on which Shaw is running his consultation but he did not want to offer a view at this stage.
The consultation process involved 14 events including a meeting in the Auckland Town Hall on Friday.
Tonight he is speaking in Gisborne and is spending the afternoon inspecting the storm damage at Tolaga Bay.