Yes you can be charged for drunk driving while riding a bicycle. In one recent Superior Court case, a woman was riding her bicycle while drunk and crashed it into the side of a car. She was convicted of driving under the influence and sentenced to 90 days in jail.
Fortunately for this defendant, the Superior Court ruled that the police did not obtain the blood evidence properly.
The woman who was seriously injured in the crash was taken to the hospital where the police asked for her consent to a blood test. She told the police repeatedly that she wanted to speak with her father before giving an answer.
The Superior Court decided that due to the vagueness of the defendant's consent the police should have obtained a search warrant.
Therefore, it doesn't matter whether you are driving a car, riding a motorcycle or peddling a bicycle, if you have had too much to drink you can be arrested for driving under the influence of alcohol.