A safe bet refers to something that is so safe that there are no risks attached. bet原意是指“打赌”，safe bet就是一定能赢的赌注，引申开来就是最保险、最万无一失的对策或者办法，也表示一定会发生的事情。

Examples:

Dress conservatively for the office is a safe bet. 办公室稳重着装是最保险的。

It's a safe bet that Mark will be the first person to arrive at the meeting. 马克一定会是到会场的第一个人。