You really need to have a serious think about your requirements. You may be better off with your townie for fun and a moped / scooter to get you to and from work. Don't simply blow off the idea of infernal combustion power especially with your stated requirements. Be objective and realistic
35 - 45 Mph is do-able with electric HOWEVER
Safety; your townie was not designed to do 45 mph. The chassis dynamics are all wrong, your brakes will not be up to the task, there is a reason why intelligent motorbike riders wear leathers.... 45mph is an awful lot of strawberry jam to scrape off the road.
Cost;
in round figures, 500 for a motor that is up to the task
300 for the controller
and the kicker, at least 1500 for a LiFePO battery that's won't be stuffed after 300 cycles because your motor is flogging it to death