you can check this website http://www.ezdanhotels.com/
this nearest place to west bay which offers short term accommodation.http://www.ezdanhotels.com/ShortStay.aspx

second option you have is Qatar youth hotel , this is cheapest place in doha but is about 30 minutes by car from west bay
http://qataryha.net/english/index.php/accommodations
Below is the contact details
Doha B
Al-Rayhan st., Al-Lakta
Doha
Qatar Tel. 00974 44217157

If you need any further help contact me at any time on private message or email [email protected]