[...This surname means "The Place of the Bridge." From "Zubi" (bridge) and the suffix denoting locality, "aga" (place of). It may also have another meaning as some authors note that it could have something to do with a certain variety of chestnut....]
The Basque surname (and firstname) Zubia is probably also taken from the Basque word zubi , meaning 'bridge', moreover there are villages with the name La Zubia, which would mean 'the bridge', which is a likely name to give to a village.
Thus, your firstname or surname means 'bridge'. I gather that it was a surname taken from the villages called La Zubia and that it become a firstname later on.