I am not sure exactly what you are asking? As long as you do not finish the BTTW quest, you cannot begin any other discovery quest, including a bump-y ride. If you are worried about finishing within the time limits, you can go ahead and finish the back to the wall quest. A bumpy ride does not start automatically, like other discovery quests you have to choose to start it. In this case, by building the maternity store, which is what begins the quest. If you want to wait to do this quest until you know you have several days of free time to complete the goals in, you can wait to build the store until you are ready.
Again, I'm not sure exactly what you were asking. Tell me if this helps or if there is something else you want to know.
