I am excited to say that we have two Anglicans in our MA program (hello if you're reading :-) The significance of Christian tradition has come up a few times in the biblical interpretation course and eventually, I was asked exactly what the Wesleyan Quadrilateral meant to Wesleyans. For good or ill, here is my general, but slightly expanded response.
Most Wesleyans in our small churches (about half our membership) are basically fundamentalist or pre-modern in their use of the Bible--little sense of any role for tradition (although it's always there whether we realize it or not). Most Wesleyans in our larger churches (the other half) are broadly evangelical, again with little sense of any role in their conscious thinking for Christian tradition, although we do have some emergent churches who are into the ancient-future trend that does highly value tradition.
I would also divide seminary trained Wesleyan ministers and leaders into two broad types. What I call Calvino-Wesleyans are again broadly evangelical or fundamentalist who might be interested in key Protestant figures as interpreters of Scripture but who are still overwhelmingly focused on the literal meaning of the text as the be all and end all of the truth process.
I'm not sure what I would call the other group but I have in mind here Wesleyan leaders that either because of our revivalist stream sit more loosely to the literal meaning of the text or who have come to see tradition as a major factor in any Christian appropriation of the biblical text (and thus who sit more loosely to the literal meaning of the text). So the experience of the Spirit and the tradition of the Church can play a much larger role in the truth process.
Perhaps all that amounts to say that there is a spectrum of Wesleyan use of Scripture ranging from fundamentalist to evangelical to emergent to pneumatic to mildly postmodern. And all of them affirm that the Bible is without error--the church never having identified a hermeneutic by which the divine meaning of the text is properly to be identified.