Hi A.,

There are bike rental options available with the railway companies (NS in the Netherlands and SNCB in Belgium), but it is not possible to return a Belgian bike to the Dutch system or vice-versa. You may do so between cities within the same country at an extra cost (normally, you would need to return the bike to the original location). You can check more details on https://www.belgiantrain.be/en/station-information/car-or-bike-at-station/rent-a-bike-at-the-station and https://www.ns.nl/en/door-to-door/ov-fiets/  . 

Try Donkey Republic.

For anyone still reading: whereas renting these OV-bikes in NL can be done at many stations, it is ONLY allowed to do with a personal chipcard with inscription for bikes, hence not open to casual tourists/travellers. The bikes are distinct blue/yellow and cost less as 4€/rent/day. They are meant for train travellers doing some short trips where bus/tram would be too complicated