See Section 128.O. Apiaries [Council Bill 55-2010 (ZRA-117)] (page 360 of the PDF) 

(Note: Please check the Howard County Regulations for any updates.  The following is an excerpt from those Regulations as of 2013)

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N. Apiaries
1. Apiaries are permitted as an accessory use on lots containing community gardens, sites where apiaries will form part of an educational program, and on single-family residential lots; and

2. An apiary that is a permitted accessory use under this Subsection shall meet the following requirements:
a. The minimum side and rear setbacks are 25 feet from the lot line, except that the minimum setbacks are 10 feet if the apiary is located as to direct the entrances away from neighboring properties and located:
(1) At least 6 feet above the ground; or
(2) Behind a solid fence, hedge, or other barrier that is at least 6 feet in height and runs parallel to the property line, and extends 10 feet beyond the apiary in each direction.
b. Bee flyways shall be at least 6 feet above any deck or other open outdoor structure that is located on an adjoining property within 25 feet of the apiary;
c. The minimum front setback is 50 feet from the front lot line;
d. A water supply shall be provided to minimize honey bees from seeking water off-site, and
e. Apiaries shall comply with Maryland Department of Agriculture Regulations as they pertain to beekeeping, and be operated and maintained in accordance with Best Management Practices; and

3. An apiary use may not unreasonably interfere with the proper enjoyment of the property of others, with the comfort of the public, or with the use of any public right-of-way.

For more Regulations go here for Federal and State Rules