You can make it work. Use 1 - 2 of your outdoor rides for gradually longer distances. Use your spin classes/indoor cycling a couple times a week to maintain your fitness when you can't ride during the week and as interval training.

What's your longest ride now? Build from that 5 + miles per week for as many weeks until 2 weeks before the century until you have a ride of 80 miles 2 weeks before the century.

In other words, if your longest ride is 30 miles and (let's say) there are 9 weeks til the century, then add 5 - 10 miles per week until you hit a long ride of 80 miles or so.

Also, what's the terrain of the century? If there's substantially more lcimbing than your usual training rides, then you will need to train for that. If there's less climbing, then you are ahead of the game!

As you are building your ride endurance, also find out what works for you and doesn't work in terms of nutrition and hydration. Training rides are the time to experiment with new foods, gels, drinks, whatever. Century day is not the time to experiment. Same with clothes. Test out new shorts, shoes, gloves, etc. on your traiing rides.