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Casinos routinely send (and accept) large amounts of money via wire transfer.
Some might have a minimum amount for the wire, based on processing fees ($25-$50 typically), administrative effort, and their preference for cash or checks for smaller amounts. These generally vary by property, state, and whether it's a land-based or online casino, but $10,000 seems to be a common cutoff point, while some casinos will wire $5,000 or so as a courtesy (to rated players). Likewise, casinos limit the maximum amount of a transfer (we've seen $100,000 per day).
You've already given the casino your ID and Social Security Number when you hit the jackpot to comply with IRS reporting and anti-money-laundering regulations. Now, you have to fill out a wire-transfer authorization form, on which the casino collects your banking details -- bank name, (sometimes) address, and domestic wire routing number (often different from ACH routing numbers or the SWIFT code for international wires) -- and your bank account number.
Transfers take one to five business days, including the time for the casino to effect the wire, sometimes immediately, sometimes in a day or so.