It depends on the minhag of the place where Bracha lives — i.e., if the minhag in that place is to allow riding scooters on Shabbos, then Bracha can ride it.
[This article deals only with a question of riding simple children scooters that don’t have inflatable tires. The question of riding a scooter with inflatable tires needs to be addressed in a different article.]
Source
Sefer Shemiras Shabbos Kehilchosa writes: “One should not prevent a child from riding on a tricycle [on Shabbos], inside a house or outside of it, in a place that has an eiruv, if the wheels of the tricycle are made from solid rubber. The same rule applies to non-electric scooters...”
Having said that, Shemiras Shabbos Kehilchosa mentions that one should not be lenient in a place where people have a minhag to prohibit riding on such toys.
* * *
[It is interesting to note that Shemiras Shabbos Kehilchosa also writes that one may not ride on a regular bicycle even if the wheels are made from solid rubber; and even if it is a type of bicycle that is made specifically for children.]
מִזְמוֹר שִיר לְיוֹם הַשַבָּת. טוֹב לְהֹדוֹת לַה ‘וּלְזַמֵּר לְשִמְךָ עֶלְיוֹן.
A mizmor song for the day of Shabbos: It is good to thank Hashem... Tehillim 92:1-2
Why is it fitting to say “It is good to thank Hashem” specifically in the perek that is recited on Shabbos? In contrast to other days of the week, a person is not busy with worldly matters on Shabbos, and his neshama is not burdened by physical exertions on his body (see peirush Radak*). Thus, this perek is saying that Shabbos is the best day of the week for giving thanks to Hashem, since on Shabbos, a person has more time and ability to do so.
*וז“ל יום השבת הוא טוב לה' משאר ימי השבוע, כי האדם פנוי בו מעסקי העולם ונשמתו זַכָּה מטרדות הגוף ומתעסקת בחכמה ובעבודת האלקים.
* Note: Menucha’s answer is for Torah learning purposes only and not as a halachic ruling. The opinions of the sources cited in the article may not necessary reflect rulings of other halachic authorities.
Tehillim
- שמירת שבת כהלכתה פרק טז אות יח (מהדורה חדשה)
- שם.
- שם.