You are also not legally required to use a child seat in a taxi, so if you're comfortable holding your child on your lap, you can use a taxi without hauling the seat around.

If you do take a bus, one thing I love is the bus tracker web site. You can check it online or a web-enable phone. It's surprisingly accurate. The transit chicago site mentioned is good too. I believe the google maps transit directions also works well.

http://www.ctabustracker.com/bustime/home.jsp

Taxis will be available anytime with no waiting, but will definitely be more expensive (versus a several day pass) if used often. Buses may be cheaper, but you will have to wait for their arrival, they stop at almost every block, and if they are crowded, having to hang on while standing and holding a baby will be tough.