take a bike for work?

Maybe you shall say:
Take a bike work,骑自行车上班。or take a bike to work.
I can not find an explation for "take a bike for sth"
I can find an example:take a bike trip.
So I think maybe strip away the for is ok.

go to work by bike
你那样不对的

好像不可以这么表达，正确说法如下两种：
1. go to work by bike
2. cycling to work

go to work by bike。

对，

不对。