Is it permissible for my wife to travel with me to Mecca to perform Umrah immediately after our return to Riyadh, or is it necessary for her to wait several days?

You may travel with your wife directly to Makkah, or wait for several days. The matter is flexible. If you are asking about the Miqat, if your wife is coming to reside in Riyadh, then there is no harm in her performing Ihram from As-Sail Al-Kabeer, and she is not obliged to perform Ihram before that, even if she passes another Miqat.