Safety
All outdoor activities carry risk. Following good safety protocol can help reduce risks, but not eliminate all risks.
Bike Safety
Probably the largest danger to bicyclist is vehicle traffic. It's highly recommended to always ride with a daylight visible rear blinking light when cycling on roads with traffic. Always wear a bicycle helmet and obey traffic laws. On remote trips carry a proper bike maintenance kit so you don't end up walking out. Carry spare clothing and/or space blanket in case of injury. Make sure to double-check bike operation before heading out (tire pressure, drivetrain, brakes, wheels true, etc.).
Paddle Safety
Know your limits. Don't paddle beyond your abilities.
Loading a bike or other gear onto a packraft creates significant risk due to entrapment and loss of boat control. Be sure to practice paddling your loaded boat in a pool or other controlled setting before heading out on a trip. It will likely be impossible to right a fully loaded capsized packraft without going to shore. Make a plan based on practice sessions in a pool.
Learn how to paddle your packraft without loading a bike at first (see Lock-n-Paddle/Paddle-n-Unlock). Become competent at paddling an unloaded boat before progressing to a loaded boat.
Know as much as you can about the route ahead of time. Are there large rapids, log jams, or mandatory portages, etc.? What is the water flow? What is river class? Has the river changed recently?
Use the buddy system as much as possible. Don't travel alone. Learn from more experienced paddlers.
Have the proper safety gear and repair kit. Wear your PFD and practice flipping and getting back into your boat (wet exit/re-entry) ahead of your trip (ideally in summer on a lake or in a pool).
File a float plan with someone so they know where you are and when to expect you back.
Take a packraft safety class or other whitewater safety course.
Take into account the wind/weather forecast on open water trips. Packrafts are heavily influenced by wind so check the forecast before heading out on open water (i.e. Puget Sound). A boat leash and/or paddle leash may be appropriate safety gear for open water. Leashes are NOT appropriate for rivers.
Read The Packraft Handbook by Luc Mehl & Sarah Glaser
Communication
These devices are a last resort. If everything goes wrong and you need assistance they may help aid in rescue. In remote areas it may be a long time before aid can arrive.
VHF Radio: On Puget Sound the best option for rescue may be carrying a portable marine VHF radio to call for help. This puts you in touch with other mariners that may be in close proximity to you and the Coast Guard.
Cell Phone: Cell service may be good in many areas close to civilization, make sure your battery is charged before heading out or bring spare charging. Protect your phone from water and keep it close in your PFD in case you get separated from your boat/gear.
Satellite Coms: Satellite communication devices can extend communication in more remote areas. There are several models to chose from to check in with friends/family or request help.