To ride versus to be riding
The simple marked infinitive "to ride" (to sing, etc) refers to the action outside of time, to the bare idea of the action, if you will. The continuous to be riding refers to the action happening in time, emphasizing its experiential or ongoing aspect.
You might hear a sentence like the following:
A funeral is no time to be playing a video game on your phone!
from a parent scolding a youngster who is in the act of playing a video game, and a sentence like the following:
A funeral is no time to play a video game on your phone.
from a parent who is calmly explaining to a youngster what is appropriate behavior at a solemn occasion. The youngster might be at the dinner table, say, and not playing a video game at that moment.
P.S. Such choices reflect the thoughts in the speaker's mind when the words are coming out of the speaker's mouth. If, at the dinner table, the parent is imagining their child playing a video game at a funeral, and the image is vivid in the parent's mind, the parent might well say to be playing even though there is no video game being played at that moment. Or the parent could be emphasizing the experiential aspect to make the lesson more vivid in the child's mind. These nuanced differences have a variety of motivations, which can often be subconscious, not consciously planned by the speaker.