+1

You're unlikely to get injured training on a properly fitted bike. (Please do be sure to have someone check your fit - even if it's just an experienced friend or acquaintance)

Time is actually more important on a bike than km. A lot of extraneous factors can make a given distance harder or easier (e.g., a rolling 10km ride is significantly harder than a flat 10km ride). In general, time will give you a better measure of the amount of strain you actually put on your body.

You didn't say what type of terrain this ride will cover. If it involves a significant amount of climbing, you will want to work some climbing into your training.

Also, I feel it's very important to get used to riding two consecutive days. In particular, make sure that you're used to riding the day after a hard ride - it can feel a little different than riding when completely fresh.

It's not necessary to ride the exact distance of the ride prior to the event, but it might not hurt to try it. 100km (if flat) is not that long a distance to go.

w.r.t. rest days and tapering. Tapering is not necessary unless you're racing. Rest days: It sounds like you're primarily riding on the weekend - as long as you're not riding more than 5 days a week, you should be getting plenty of rest. In fact, if you're only riding on the weekend, I'd advocate trying to do a mid-week ride or two, even if they're only a half hour.

Also, you may want to try doing some group rides. There are big benefits to be gained in riding in groups where you can draft a little. Most larger riding events will have enough riders that little groups will form - it's best to have some experience riding in groups prior to the event.