答案是while,while+doing,表示一个动作正在进行；
如果填since的话,应该是
Excuse me,did you notice whether the No.108 bus had gone by?
No,since I was （standing） here.
因为since（自从）引导的从句,不能用完成时态,只能用一般过去时态；
当然since（由于）引导的从句,就另当别论了,但是这个,since不是这个意思；
ps：答语是一个省略句,即：
No,I didn't notice while I have been standing here.所以这个题目出现了一个小小的错误,
这个while应该是和notice保持时态一致的,所以建议把题目稍作调整：
No,I didn't notice while I had been standing here.或者
No,I didn't notice while I was standing here
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