Bikes taking up space for customers of the public transport is a false myth.
The reality is that public transport which does not offer convenient free bike transport will never see those potential customers on board.
Copenhagen S-train (metro) has shown that since the introduction of the possibility to transport for free the bicycle on S-trains in 2009, the customers increased abruptly.
It worked so well in Copenhagen that they removed seats to make more space for customers. http://www.cycling-embassy.dk/…/x-tra-bikes-on-the-s…/
Public transport company DSB understood that is possible to increase your paying customers by offering a convenient service, not a simple seat (which will stay empty if you are not offering what the customer need, and in Copenaghen, customers need to take their loved bike along).
http://www.copenhagenize.com/2016/11/massive-passenger-increase-after-bikes.html
Bikes on bus?
While it makes sense to take the bike on a train (on a long route), it does not make sense to take it on a bus for a few kilometres. Built the bike lanes, and there is no need to carry bikes on buses.