I assume you have a car?
The best beaches are east of Almeria city, especially in the Cabo de Gata national park. But that is much longer than your 90 minute limit. It still might be worth considering if you are willing to make a (very) long day of it and, perhaps stop off on the way in Almeria province's "desert zone". It is quite an attractive landscape in a bleak type of way. Very photogenic.
Whatever you do, avoid the stretch of coastline between Motril and Almeria city. It is mostly a grim expanse of plastic greenhouses for the fruit industry.
Perhaps best, and within 90 minutes, but not 60, is the stretch west of Motril. For example sleepy La Herradura; or Salobrena which is bigger and more touristy but still pleasant; or Almuñécar which is more built up, but does have some sights as well as the beach, including an excellent castle, and will certainly have operators offering snorkelling and other activities.
PS I've never been to Bubion, but we did once stop in Capileira, which is an attractive village you might want to walk to one day.