Sidon or Zidon = "hunting"
an ancient and wealthy city of Phoenicia, on the east coast of the Mediterranean Sea, less than 20 miles (30 km) north of Tyre (see map)
derivation:  of Hebrew origin (06721)
http://bible.crosswalk.com/Lexicons/Greek/grk.cgi?number=4605&version=kjv

(06721)
Sidon = "hunting"
derivation: from (06679) in the sense of catching fish
http://bible.crosswalk.com/Lexicons/Hebrew/heb.cgi?number=6721&version=kjv

(06679)
1] to hunt
   1.a] (Qal) to hunt
   1.b] (Poel) to hunt, hunt eagerly or keenly
   1.c] (Hithpael) take provision
http://bible.crosswalk.com/Lexicons/Hebrew/heb.cgi?number=6679&version=kjv

Additional information:
"Saidoon is the Phoenician name, Saida in Arabic."
Quoted from: http://www.middleeast.com/sidon.htm

Comment:
It therefore seems that "Bethsaida" means "House of Sidon", that is, "house of hunting".