Do I have that same luxury in this situation?
Yes you can do a rollover but watch the 60 day rule, especially if you can't just walk into the bank branch to start or complete the transaction. The days the check is in the mail count.
The new and the old account will be locked out for a year, meaning they can't be involved in another roll over. They can be involved in a direct transfer, or a transfer . Make sure that it has been a full year since a rollover involving that account.
The distribution can be full or partial, and the target account can be new or existing. Make sure that the account types are the same traditional IRA to traditional IRA or Roth to Roth. Otherwise you will be doing a recharacterization which will involve additional forms and taxes.
The roll over can bridge from one tax year into another, but make sure the IRS is knows that is the way it worked.
If I sell some of my IRA, then later move my bonus into the same account, have I
effectively avoided any taxes at all on the IRA withdraw?
From the IRS: The same property must be rolled over. If property is distributed to you from an IRA and you complete the rollover by contributing property to an IRA, your rollover is tax free only if the property you contribute is the same property that was distributed to you.
Cash is cash, but you can't claim that you deposited X% of the house.
If not, can I roll this money into my wife's IRA to achieve the same
Your wife can roll her funds from one account she owns into another account she owns. Thus achieving the same tax free short term borrowing . But you cannot move funds from your account into her account. There is mixing of the funds, unless you inherited the account from your spouse.
withdraw up to $10K from your IRA for a qualified first time residence purchase
This could be used as an emergency. If you pulled 25K from the account, but as the sixty day window was about to close, you could only come up with 15K the rest could be considered for the purchase of a 1st home. There are additional rules and timelines involved. Determine if this is possible before making the disbursement.