In nearly everyone's mind the word service is followed by "to someone" or to some cause. It is a voluntary act, in the sense of "helping", "doing a favour", "being useful". It usually supposes a return, as in "something for something", even if that is implicite.

Unmotivated service is something else. It's an act of kindness only meant to please, or to promote a noble cause out of the goodness of your heart. It is done without any idea of receiving an advantage other than the satisfaction to ahve done it. This one is known as selfless service and it is rare.

Besides all this, there is service to God. This one may be subject to caution because it is more elusive, more easily abused. Bhakti is the sanskrit word for Devotional Service. In the timeless Bhagavad-gita, the blessed Lord is said to teach mankind :

"Whatever you do, whatever you eat, whatever you  give away, and whatever trouble you take – do it as an offering to Me." (9.7)

Bhakti is devotion of an active kind, not just a sentiment. If you hear me say, "I love you", you have every right to expect action behind the declaration. Without high regards, best behavior, unfailing care and kindness, how will anyone believe in you love them?

Neither will God. Let's say I only imagine my work to be pleasing to God. According to the above quote, whatever work you do can be offered. Beyond personal maintenance,  your wages too can be offered. This too is counted as bhakti.  Whatever you cook and eat can first be sanctified. Christians sanctify food by saying Grace before their meals, Hindus place a sample of the meal on their altar for their Deity to eat it first. Each to their own, the result is always devotion.

Personal or impersonal doesn't matter here. Should Divine Energy be less capable of responding to bhakti than a personal Deity?  You'd have to insist that Divine Energy is beyond love and care. Even if it were, your intention of behaving in harmony with the universe counts as much as anything.

Is service to others bhakti? You need no religious belief to do good to others. The only difference between that and bhakti is your consciousness. Service to humanity with the awareness of its connection to the larger universal reality is best. Just imagine the feeling of being connected to a conscious universe.