The Dead Sea coastline stretches for about 31 miles (50 km), but from Aqaba to the northernmost point is a 170-mile (273 km) trip. It's three hours by car and you'll take Route 65 the whole way, typically with a private transfer or taxi.
Taking a bus is the least preferred choice and can take double the amount of time. There is no direct public transport (minibus) so you'll have to take a JETT tourist bus all the way to Amman first. From Amman, it'll be a combination of minibus and taxi ride the remainder of the way to Amman Beach.
Many of the luxury resorts on the coast have clean, private beaches and sell day passes for non-guests. Amman Beach is a decent public option, though you can expect it to be crowded and there is an entrance fee. If driving, consider taking a detour to other attractions along the route, including the Dana Biosphere Reserve, Wadi Mujib or Karak Castle. These scenic road trip ideas might provide some helpful insight as you plan.
By Private Transfer
Duration: 3-4 hours
The scenic drive along modern Route 65 can be done in about three hours—but since you'll have the freedom of your own vehicle, it's worth taking your time to sightsee along the way. Hiking the wilderness trails at Dana Reserve or Wadi Mujib is one way to break up the drive. Karak Castle, an enormous Crusader castle built in the 1100s, is also a good stopping point for stretching your legs and taking photos. Once you get to the coastline, you'll have your pick of seaside resorts and beaches and your guide may be able to offer suggestions to lesser-known spots away from the crowds.
Duration: 3-4 hours
If you want to leave the driving (and parking) up to someone else, consider catching a taxi out of Aqaba. They're very easy to find and your hotel can book one in advance for you. Shared taxis often mean a cheaper rate which may be a bonus for the budget-minded individual traveling solo. If you want to get the most out of your trip, there's always the option of hiring a taxi for the entire day so you can visit multiple attractions. Don't forget Ridesharing apps: Uber drivers are gaining traction in Jordan and your costs might be even cheaper than a taxi.
Duration: 6-8 hours
While the minibus is generally ubiquitous, no direct route is available between Aqaba and any points along the Dead Sea. You'll have to catch one of the daily JETT tourist buses to Amman. It's cheaper than a rental car and runs frequently, but the journey will be long and fairly inconvenient so plan ahead if you're on limited time. Tickets can be booked in advance on the JETT website. The ride to Amman's Abdali Station will take about four hours, then you'll have to switch to a minibus to Rame. At Rame, disembark and take a taxi to your desired location.