What traditions believe that a woman's relationship with God must go through some man and how do they support it from the Bible?

I think a better way to word your question is "What traditions hold the most conservative view of 1 Corinthians 11. If any tradition or denomination stands by what you are saying, they would most certainly derive the Biblical basis from this passage:

But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.Every man praying or prophesying, having his head covered, dishonoureth his head.But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven. For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered. For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man... For this cause ought the woman to have power on her head because of the angels. 1 Corinthians 11:3-7,10 (emphasis added)

I don't think any present, mainline group would confirm that a woman's relationship with God must go through a man. Even the most conservative denominations today would emphatically state that women participate equally in the priesthood of believers. What differs is the role that women play in the Church (at this point, I wonder what your sources are that brought up this question. Please see below for a commentary from Matthew Henry on this passage. Although your question does not necessarily warrent this, I think it's helpful to see a very traditional, mainline view from the 1600s.)

That said, I have met individuals, even pastors who stand by this "must go through a man" line of doctrine. It's spoken of as "headship," that a women must have a male "head" that represents her. This can be a pastor, father, or husband that agrees to take responsibility for her spiritual growth. What ends up being the case however, is just a de facto acknowledgement of headship, almost like "nearest of kin" laws: If a woman has no husband, then her head is her father, if he's not a Christian, the her pastor, and so one. It really is not an active headship unless the women consents to it or it's forced. Again, it's not a commonview.

What this purported view of women sounds like, really, is the convention of coverture, a principle in English Common Law that subsumes a married woman completely under her husband. Under this law, a married woman could not own land or make legal agreements (even commite a crime) without her husband taking responsibility. As has been the case for centuries, religious and civil principles have been confused and and convoluted, so while it may seem like this is a current view, it's actually a relic from Medieval times.

The thing he reprehends is the woman’s praying or prophesying uncovered, or the man’s doing either covered, v. 4, 5. To understand this, it must be observed that it was a signification either of shame or subjection for persons to be veiled, or covered, in the eastern countries, contrary to the custom of ours, where the being bare-headed betokens subjection, and being covered superiority and dominion. And this will help us the better to understand,

... though a woman might not from her own abilities pretend to teach, or so much as question and debate any thing in the church yet when under inspiration the case was altered, she had liberty to speak. Or, though she might not preach even by inspiration (because teaching is the business of a superior), yet she might pray or utter hymns by inspiration, even in the public assembly. She did not show any affectation of superiority over the man by such acts of public worship. It is plain the apostle does not in this place prohibit the thing, but reprehend the manner of doing it....

To understand this, it must be observed that it was a signification either of shame or subjection for persons to be veiled, or covered, in the eastern countries, contrary to the custom of ours, where the being bare-headed betokens subjection, and being covered superiority and dominion. And this will help us the better to understand, The reasons on which he [Paul] grounds his reprehension. 1. The man that prays or prophesies with his head covered dishonoureth his head, namely, Christ, the head of every man (v. 3), by appearing in a habit unsuitable to the rank in which God has placed him. Note, We should, even in our dress and habits, avoid every thing that may dishonour Christ. The woman, on the other hand, who prays or prophesies with her head uncovered dishonoureth her head, namely, the man, v. 3. She appears in the dress of her superior, and throws off the token of her subjection. She might, with equal decency, cut her hair short, or cut it close, which was the custom of the man in that age. This would be in a manner to declare that she was desirous of changing sexes, a manifest affectation of that superiority which God had conferred on the other sex. Henry, Matthew. "Commentary on 1 Corinthians 11." . Blue Letter Bible. 1 Mar 1996. 2011. 29 Aug 2011.