I have been cycling for one summer, around 80-100 km a week, mostly heavy hills and I did not gain a single pound of muscle that summer. I was eating a lot and lifting 6 day a week.
I was riding 2-2.5 hour 3 times a week and sometimes adding a 50-60 km run on the weekend. This is not a lot by cyclist standard, but that was killing my BB progress for sure.
If you have a racer type bike and there is no hill on the road, I would say it may be ok but do not push it, but let see it:
Riding a quality racer at 25 km on a straight road is pretty easy, almost effortless, like walking, I would say even easier than walking. You will do the 13 km in 30 minutes.
That 60 minutes of low intensity steady state cardio 3-4 days a week split in 2 sessions. You look like a beginner, so I would say, yes it's possible if YOU EAT ENOUGH and rest.
The problem, if you are like me, is that if you buy a racer, you will want to ride it fast, you will buy those clip pedal and say to yourself 'Why going at 25 km/h when you can ride it at 40? Fuck it!' And this is the beginning of the end and you will hurt your BB progress
Here is a picture of my racer