To find Recycle bin in start menu search as you asked is explained very detailed here with screen caps.
Hope that post useful to you.I have tried in my comp and it works like follows.
In My computer or Windows explorer type these in navigation toolbar C:\Users\Desingh(type your user name)\AppData\Roaming\Microsoft\Windows\Start Menu
Right click, create new shortcut and enter this
And name the shortcut as " Recycle Bin" and click finish
Now type Recy in search bar it will show the Recycle Bin shortcut link
It shows me like this.
If you want to change the icon of Recycle Bin link you can do it by the procedure given above link but not necessary .