Bicycle and bus bombs kill 8 in Iraq

* Cycle bomb kills 5, wounds 37 in Mussayab south of Baghdad

* Bomb on bus leaves at least 3 dead, 15 wounded in Kerbala

(Adds bomb in Kerbala)

BAGHDAD, Nov 1 (Reuters) - A bicycle loaded with explosives killed five people and wounded 37 at a market in Mussayab, south of Baghdad, on Sunday and a bomb on a bus killed at least three more further south in Kerbala, police and health officials said.

The explosives in the first attack were stored in a water cooler attached to the bicycle, and women and children were among the dead and wounded, police said.

Mussayab, 60 km (40 miles) south of Baghdad, is home to both Sunni and Shi'ite Muslims, but the town centre where the explosion took place is mostly Shi'ite.

Fifteen people were wounded in the second incident, hospital officials in the Shi'ite holy city of Kerbala, 80 km (50 miles) southwest of Baghdad said. One of the dead was a police officer at a checkpoint the bus was driving towards. Some police sources put the dead at five.

The attacks bore hallmarks of Sunni Islamist insurgents such as al Qaeda, who often attack crowded, mostly Shi'ite areas, but many Iraqis also fear an increase in intra-Shi'ite rivalries ahead of a parliamentary election in January.

Overall violence has fallen sharply in Iraq in the last two years, but bomb attacks and shootings remain common. Two suicide bombings killed 155 people and wounded more than 500 in Baghdad last week.

Iraq is due to hold a general election on Jan. 16, and insurgents are widely expected to try to upset an electoral process that is taking place as U.S. troops pull back ahead of a full withdrawal from Iraq in 2011. (Reporting by Khaled Farhan in Najaf and Sami al-Jumaili in Kerbala; Writing by Mohammed Abbas; Editing by Louise Ireland)