Can I carry a bike on the bus to the airport in Rotterdam?

No, taking a bike on the bus is not allowed with any of the bus operators in the area: RET, Veolia and Connexxion, except for folded foldable bikes (IIRC the bus from Rotterdam Centraal to the airport is currently operated by RET). There isn't that much space in the bus either.

In fact, bikes are so ubiquitous in the Netherlands that it's simply impossible to allow them in public transports.

If you have a bike that can support your luggage (i.e. you are bicycle touring, which I assumed initially) or you have a single item such as a backpack you can carry while biking you should just ride to the airport from Rotterdam centre. Less than 20 minutes, cheaper and easier. All routes google maps suggests are fine and will get you there over bike-paths or roads that have ample space for cyclists.

However, if your bike does not support luggage or you have too much of it, I assume you'll be packing the bike for transport on a plane. If that is the case then probably you can take the bus. Bikes are not allowed, but luggage is. This is not just a nitpicking thing. If (as another poster said) bikes were allowed on buses all hell would break loose in the bus on days with unexpected rain in the afternoon (50% of commutes in the netherlands is done by bike). On the other hand everybody understands your need to get your packed bike to the airport in one piece.

No Non-Foldable Bicycles on Buses

Looking on the English version of the RET website, I found the General terms and conditions urban and regional public transport 2014 which explicitly mention bicycles on trains and subways, but not buses. I think it is safe to assume that non-foldable bicycles are not allowed on buses, since these are not mentioned in the terms and conditions:

Bicycles

4.9 Unless expressly prohibited by the transport company, you may bring a bicycle with you on a train in the areas designated for that purpose on the condition that sufficient room is available for it in the judgment of the transport company.

4.10 Unless expressly prohibited by the transport company, you may bring a bicycle with you in the subway in the areas designated for that purpose on the condition that sufficient room is available for it in the judgment of the transport company.

4.11 If the transport company indicates that a fare is owed for transporting a bicycle, you must be able to present a valid ticket for it.

Say Yes to Foldable Bicycles

There is also the mention of foldable bicycles as hand-luggage, which are apparently allowed on public transports if there is enough room for them:

Hand luggage

4.5 You may bring hand luggage (including a folded foldable bicycle) with you on the condition that sufficient room is available for it in the judgment of the transport company.

4.6 The transport company may deny you access to the vehicle or ask you to exit it, if, in its judgment, your hand luggage could represent a danger, pollution hazard or inconvenience for others.

It follows that you should be able to take a foldable bicycle on the Airport bus, if the driver deems there to be enough space for it. This is also in accord with this Holland bicycle-fanatic website:

Buses in Holland will only take a folding bicycle. You have to fold it outside the bus and carry it inside as luggage. Some bus companies specify sizes, others require you to put your bike in a bag. Basically, if you have one of those bikes that fold up really small, you’re OK. If you have a less compact folding bike, you are dependent on the goodwill of the driver. In general, it may be easier and quicker just to cycle to your starting point.