He also put up some signs asking for old bikes.为什么用asking不用t

He also put up some signs asking for old bikes.为什么用asking不用to ask?
还有waste time doing sth和这个是一个道理吗

不一样.
asking for old bikes是作定语修饰signs.=定语从句which asked for old bikes
如果改为to ask就看作是目的状语了.
waste time doing sth 意思是“浪费时间做某事”
doing sth是作宾补的.类似的有spend time doing sth.
祝你学习愉快!