We’d say you’ll be pretty safe. Strip traffic tends to be slow and, in 2013 (the most recent year for which we have statistics), there were only seven cycling fatalities in Nevada as a whole, which is pretty surprising when you see the crazy way people in Vegas tend to drive. While seven fatalities is seven too many, Nevada compares quite favorably to the national total of 743 that year.
However, earlier this month a bicyclist sustained "critical injuries" after being rammed from behind by a car at Las Vegas Boulevard South and Spring Mountain Road, an accident that closed the southbound Strip for five hours. The cyclist lingered between life and death for 10 days before expiring on August 13.
But if you still want to bike it, you can find parking at SLS Las Vegas, on the first level of the Paradise Road entrance. Palazzo has valet parking for cyclists and has had it since 2008, as does sister property Venetian. Treasure Island has bike parking spaces on the first floor of its garage. (Unless otherwise indicated, bike-parking areas are on the ground floor of casino garages.)
Strip casino-hotels that don’t have bike parking are Bally’s, The Cosmopolitan of Las Vegas (is that "the right amount of wrong"?), The Cromwell, Harrah’s, MGM Grand, Monte Carlo, Tropicana, and Vdara. Elara won’t park your bike but will store it in the luggage area. Similarly, Mandarin Oriental will store your bike at the bell desk. Aria’s parking is in the motorcycle lot near the valet-parking area, while Bellagio would have you bring your bike directly to the valet. As for other MGM Resorts International properties, Circus Circus has parking next to the employee garage, while Mandalay Bay has it on the garage fourth floor, near the security booth. Luxor’s bike parking is at the rear of the pyramid, in the garage, and at the Mirage you can use the motorcycle racks on the fourth floor of the garage. At New York-New York, look for the "oversized" area at the rear of the garage. At Excalibur, the bike parking is between the parking garage and the rear casino entrance.
Caesars Entertainment properties where you can park your bike are Caesars Palace, the Flamingo, and The Linq (by the engineers’ shop). Paris has bike parking on every level of its garage, next to the elevator banks. Planet Hollywood has it near the ground-floor elevator and the Rio’s is on the west side of the property (ask the valet for directions).
You can park your bike at Trump International, but you can’t secure it to anything. Casinos that do have racks are Casino Royale, Hooters, the Palms, Stratosphere, and Westin Las Vegas. Last but not least, Encore provides bike parking on every level of its garage, while Wynn Las Vegas has it on the second floor of its south garage. Happy riding!