Schottky barrier diode as a bridge rectifier?
In this application Schottky diodes will work just as well as normal diodes, by arranging them as you normally would a bridge rectifier. They are not normally used in regulators because they are more expensive and sometimes physically larger. The advantages of a Schottky diode (low forward voltage, fast switching) will not provide any benefit for an ordinary bridge rectifier.

The best option for hobby projects is to get a purpose made bridge rectifier that has all of your rectifier diodes integrated in one package. These cost about $2 in small quantities.

However, the specific part you have selected should not be used in a 120V bridge rectifier, because it will experience a peak-to-peak reverse voltage of 336V, well above the maximum rated 150V reverse voltage for this part. Don't do it.

And make sure you have a GFCI or isolation transformer between mains and your power supply.