As you suspected, the ますform for a verb like 走る, 走ります, is different from the ます form of a る-verb like 食べる, which becomes 食べます.
Unfortunately, there is no way to distinguish what type of る-verb you have from its dictionary form alone so you are going to have do some research on google each time you encounter a new る verb. However, your example sentence makes it obvious that 走る is a special る-verb because of the small つ before the て.Gradually, you will remember which る-verbs are which but until then just keep the differences in conjugation in mind so that you can identify them when reading or listening to Japanese.
走る => 走ります、 走らない、 走って、 走ろう
食べる => 食べます、 食べない、 食べて、 食べよう