The legendary B.B. King opened an outpost of his Blues Club and Restaurant at the Mirage in November 2009, but the venue was beset with financial problems from the get-go and closed three years later. And while the House of Blues at Mandalay Bay is alive and kicking, its typical band line-up seems to feature pretty much everything except blues! So, that pretty much rules out the Strip as far as what you're looking for.
However, Las Vegas is still home to a pretty vibrant blues scene -- you just have to know where to look for it and your best bet is the website of the Las Vegas Blues Society, which lists all the venues (mainly of the dive-bar ilk) that periodically or regularly feature live blues, plus band bios and an event calendar which, from experience, is kept pretty up-to-date and accurate.
For many years -- on and off -- there was a venue on Spring Mountain a block west of the Strip (and a block east of the LVA offices) called The Sand Dollar, which was a popular down-and-dirty dive bar known for its live music, where you could regularly catch long-time local blues acts like John Earl and the Boogeyman Band. After several closures and comebacks, punctuated by failed attempts at an identity change (e.g., The Bikini Bar), it's now finally reopened as Bar 702, as soon to be featured on Spike TV's "Bar Rescue," and once again is featuring live blues bands. However, be aware that the music scene here is pretty eclectic these days and features a variety of genres (from Zydeco to punk), so check the schedule before making a special trip.
The Cellar Lounge, on Sahara at Valley View, is also an established blues venue, where you (and an enthusiastic crowd of local regulars) can catch the talents of Billy Ray Charles and the Boys from the Parking Lot every Friday and Saturday night from 11:30 p.m. B.B. King himself dropped in and jammed one legendary night, as have other celebrities, including Kenny Loggins. We happened to be having a beer there a few Sunday afternoons ago, when Nicholas Cage and his wife randomly strolled in for a drink, stating that they'd been told, "This is the place to be." (Sadly, whoever told them this had evidently failed to explain when it's the place to be, and a few regulars catching a soccer game probably wasn't exactly what they were looking for.)
In addition to regular and irregular shows around the valley, Las Vegas also hosts some music festivals that you might like to check out. You just missed the annual Blues and Brews festival, which took place at Springs Preserve earlier this month, but this September 15-17, the Rio is scheduled to host the Sin City Soul and Blues Revival, a three-day festival featuring 40+ bands playing on three indoor and one outdoor stage, with headliners including Tedeschi-Trucks Band, Los Lonely Boys, Tab Benoit, and other. See sincitysoulandbluesrevival.com for details and tickets.