Yes, with proper training, you can do a century, or a bike tour. I'm 64, just completed a 300 mile bike tour over 5 days in Nebraska. Longest day was 70 miles. There were women, and men, older than me on the tour and they rode every mile. I also know a 74 yr old woman who completed a ride across country last year. Because the ride began in March and she was living at a ski resort she did all of her training on a bike trainer indoors.

Nothing wrong with the current bike you're riding but for 100 miles of riding I suggest you get a well fitted road bike that is lighter and has better gearing for climbs.