Yes, you can ride your bicycle on the street. Per the Wichita Municipal Code Section 11.48.100, every person riding a bicycle upon a street is granted the same rights and duties applicable to a person driving a motor vehicle. However, additional special regulations apply. The special regulations include those described in the Wichita Municipal Code Section 11.48.120 which describes where and when cyclists should ride on the street.
City Code Section 11.48.100 City Code Section 11.48.120