The book which the quote is from is also being cited throughout the thesis, so naturally it is included in the bibliography.
What should the citation look like? Should it be consistent with the citation style used in the text, or is including the full title favorable?
I would not cite the quote differently than any other reference in your thesis. So which ever format your discipline uses (APA, MLA etc...) would be what you would use.
I upvoted Greg's answer, because that is what I would do, if for some reason I could not ask the relevant authorities.
Your first step should be to get a copy of the thesis formatting guide or manual of your institution. Most universities have one.
Your second step, if this guide does not answer your question, should be to ask the examination authority of your institution.
Your third step, if the examination authority is unable or unwilling to provide a definite answer, should be to ask your professor(s).
If, for some unimaginable reason, you still have not been given an answer, do as Greg said.
