how long does the side affect last on the depo shot

According to this link,

"The side effects are usually not serious, but it is important to realize that once Depo-Provera is injected, it cannot be reversed or neutralized. You will have to live with the side effects until the medicine wears off in 3 months."

Bleeding and spotting are among the side effects listed.

This is from the Planned Parenthood site about this drug:

"Irregular bleeding is the most common side effect, especially in the first 6 to 12 months of use.

• For most women, periods become fewer and lighter. After one year, half of the women who use the birth control shot will stop having periods completely. 
• Some women have longer, heavier periods.
• Some women have increased spotting and light bleeding between periods."

Might be for the duration. If bleeding is excessive you should contact your doctor, or discuss whether you wish to contniue using this drug or switch to  some other other from of birth control.