As the motor is only to generate vibrations (no shaft) then there is probably no need to run it forward and backward. A simple transistor will do the job tip120 transistor: controlling dc motors and lamps from the arduino | Connect the Dots The motor is only 2.5-3.8 volts so you will need a suitable way to power it. The UNO's 3v3 output is only rated to 50mA so is not suitable
Using an h-bridge can improve haptic performance (reversing the polarity stops the motor quicker), but as Riva mentioned there's no need if your doing simple vibration alerting. Tonnes of advice from the motor's manufacturer:
Discrete driver circuit
H-bridge
Integrated driver circuit
You can buy MOSFETs from tonnes of electronics shops (depending on your location), e.g. Maplin, Farnell / Element14, RS online, Radioshack. It's also worth checking Ebay, lots of sellers specialising in hobbyist electronics. For the h-bridge you can either build yourself out of transistors (actually a pretty simple build, the schematic looks way more complicated than it is), or buy an h-bridge chip.