There are (many) people that are carfree, and they do that much and more with no issues. As far as conditioning, it's going to take a while for your muscles to get used to it. Because i also run, i take a rest day (today, actually. it sucks) just to give my muscles time to rest. Something that more people need to realize is in other countries (Netherlands, etc.) bikes are the main transport for most people. They don't worry about it like we do. It's not bike commuting, cycling, or even a bike ride. It's getting to work, and running errands.

It's all up to you and your fitness level. as far as mentally, well, biking is stress relief for me. so, for me, that's not an issue.