Andy, I don't know what level you ride at and I don't need to know. I'm guessing from your OP that you're not a seasoned TT rider. Many people do TTs on road bikes.
There was a time when EVERYONE used them, as TT machines were still in the future.
You can also buy some TT bars (Tri Bars) and fool around with your seat post and stem length to get a more 'TT' position on a road bike.
The experienced riders at your club will be able to give you an idea of how much faster you'd be going on a TT bike.
Give it a go for a season and then decide. It is a strange discipline and takes quite a while to learn for something so apparently simple. You are looking to empty the tank completely over ten, twenty-five or more miles while keeping an eye on traffic, road conditions and your route. Even an experienced athlete will find themselves blowing up at three-quarter distance one week and then coming home with tons of energy unused another...
I'd spend a season getting into the physical rhythms of TT riding and then splash out if you think it's your bag.
As to doing two TTs in a week.... make that decision after doing one. It can be quite a sapping business.
Let's not get carried away here. I will often do another 10 after the club 10 to complete a good threshold 2x20ish session. That's on top of riding 25 miles to work, then twenty to the race and then another 15 to get home after. I will also do a race at the weekend. A 10 mile TT is just 20-30 minutes of hard effort. It's not a big deal.