Extension cord out of electric box for toilet seat bidet
You cannot simply use a flexible cord wherever you please (Code NEC 400.8)  particularly where fixed wiring in the walls would normally be used.   

However, one type of allowable fixed wiring is a surface conduit such as Legrand Wiremold.  

The "starter" box sits on the surface over your existing receptacle, and the surface conduit extends off its side, down the wall to wherever you need to go for the other outlet. 

If you also want more receptacles, add that to the surface conduit system. You can go 3" to another receptacle before you head to wherever you're going. 

You will absolutely need GFCI protection on something like a bidet, and the "starter" box will give you lots of room to mount a GFCI+receptacle combo device.   You can feed the bidet any other outlets from the GFCI+receptacle module, so they will also be GFCI protected.