The verb "ride" is irregular. Its three forms are ride, rode, and ridden, for present, simple past, and past participle. The sentence has the time marker "yesterday," which needs the simple past tense.
"Rode" is the correct simple past form, so "I rode my bike yesterday" is grammatically correct. The word "road" is a noun meaning a path for vehicles and sounds the same as "rode" but has a completely different meaning and spelling. "Rhode" is a proper noun, used in names like Rhode Island, and has no verb function. "Ride" is the base or present tense form and cannot describe a completed action in the past.
Since the action happened yesterday and is already finished, the simple past "rode" is the only form that fits.