I think dettol is a little bit too strong for babies so best not to spray it on baby mattress. You can use natural way of putting your baby's mattress under the hot sun then later tapping it to remove dust and hopefully dead bed bugs. Otherwise you can also invest in a handheld uv vacuum specially for killing bedbugs. You can find some on qoo10. http://list.qoo10.sg/s/UV-CLEANER?keyword=uv+cleaner&keyword_auto_change=
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You could use dettol to kill the bugs, but make sure you keep the mattress to dry in the sun for atleast a day so that the smell goes away.
I would use dettol to to clean the bed and i would sun tan it to be safer.