Bike would be fine- but will you? Takes a lot of training and fitness to do a 100 mile ride.

My first however was done on a Mountain bike with 27gears and I walked a few of the hills. Mind you that was offroad and in 94. That same year I did my first road 100miler on the same bike and just changed the tyres. Not as stiff a climb as you are planning but Did Mt. Ventoux on a basic Giant OCR3 with slightly lower gearing. Did that when I was 60 and was my first mountain.

All I can say is low gearing and get training. You will need both.