I've got a single-member LLC so it is all pass through income for taxation.
I've created a SEP IRA. When I make contributions to the SEP IRA, should it come from the bank account of my LLC or my personal bank account?
Quite confident that it doesn't matter. Many self-employed businesses do not have a business bank account at all. When you do your accounting and taxes you will say how much of the profit of the company was put into the SEP and the numbers should tie out. That's the only way the government or your provider knows where the money came from. They don't trace accounts or anything.
I have a sole proprietorship and a solo 401(k). Not only does it not matter where the checks come from, but in the case of the 401(k), my provider does not even report my contributions to the IRS. My provider doesn't know or care whether my contributions are part of the employee "elective" contribution and what part is "nonelective" profit sharing. I can tell them at the end of the year and they will make a note, but they will never tell the IRS and the IRS never asks. You should have proof that a contribution was made in case there is a doubt (easy to have these days) and you should report it correctly on your taxes, but that's the extent of your burden.
Some of the benefits of the (SEP) IRA come from the tax code. Consider reviewing the tax form you use to report to see how it becomes exempt from taxes.
I believe an LLC taxable as partnership excludes the deposits to the income to the partners.