ProVelo offers in Brussels bicycles for rent:
Pro Velo - Rental Info (English, French, Dutch)
Their main rental point is the Cyclist's House in the Londenstraat/Rue de Londres 15, 1050 Elsene/Ixelles:
Pro Velo (English, French, Dutch)
Furthermore presents ProVelo a list with 40 bicycle shops in Brussels Capital Region. I'm sure some of them are also into renting bikes, but you will have to check their sites yourself:
Pro Velo - Bicycle shops in Brussels (English, French, Dutch)
A quick look learns me that at least Vélocité in Schaarbeek/Schaerbeek
Vélocité (French), Km10 Bicycle Store in Watermaal-Bosvoorde/Watermael-Boitsfort
Km10 (French), Vélopipette in Watermaal-Bosvoorde/Watermael-Boitsfort
Vélopipette (French), Eddysport in Sint-Lambrechts-Woluwe/Woluwé-Saint-Lambert
Eddysport (French) and maybe also Van den Mooter in Jette
Van den Mooter (French, Dutch) do rent bicycles.
The Belgian Railways rent bicycles in the most important (touristic) places in Belgium, but not in Brussels. Their rental services are limited to these 12 places: Blankenberge, Brugge, Gent, Hasselt, Knokke, Leuven, Lier, Oostende, Sint-Truiden and Vielsalm. That's also more close to reality as in another post of mine I was talking about 'in most Belgian railway stations ...' Sorry about that.
Fiets ze!