If I purchase this with hard money, how soon can I take it to a bank to get it refinanced?

Try to do this so that the cashflow of 2 properties are at least the same as the 1 property before you refinanced, if not more.

I have some experience in the rental game, I owned a managed a single family for several years, but made the mistake of selling instead of refinancing it.

Through refinancing.

Refinancing and pulling out equity is one of the best tools a real estate investor can use. 

From what I've read, I see it requires a loan for repairs/ purchase price which is then refinanced.

Should have purchased it, leased it and refinanced out.

I've not once, ever, done a BRRRR-related 85% LTV cash out refinance, usually people doing that are refinancing out of FHA and into conventional to drop the mortgage insurance. 85% LTV FHA Cash Out refis are either FHA-to-FHA, or conventional-to-FHA, the opposite of what BRRRRrrrr people are doing (FHA-to-conventional)... these people are refinancing to sign up for mortgage insurance, all for that little extra 5% (they they are paying 35% of it towards fees) they want.And these are FHA loans, which means government insured, which means taxpayer on the hook.

I've not once, ever, done a BRRRR-related 85% LTV cash out refinance, usually people doing that are refinancing out of FHA and into conventional to drop the mortgage insurance. 85% LTV FHA Cash Out refis are either FHA-to-FHA, or conventional-to-FHA, the opposite of what BRRRRrrrr people are doing (FHA-to-conventional)... these people are refinancing to sign up for mortgage insurance, all for that little extra 5% (they they are paying 35% of it towards fees) they want.And these are FHA loans, which means government insured, which means taxpayer on the hook.

Also if you don't mind me asking, what is wrong with getting personal lines of credit if you have a good exit plan such as refinancing the property after a year of purchase