When you write a melody, you imply something about the harmony as well, and so you have some kind of a vague idea or gut instinct about chords, even if you can't or don't want to explicate any specific chords right away. You can do it either way. Think of chords first (for example by using voice-leading as a guideline for thinking up something) and place melody notes on strategic places in the harmony progression, fulfilling any other criteria like ups and downs, tension and release, rhythmic feel, expectation and surprise, etc. Or write melody notes straight away for example following the ups and downs and natural rhythm of lyrics, and then think of nice chords to support it while satisfying other "design criteria" like tension and release etc. Modern pop songs usually stick to colorless/tasteless/odorless minor or major pentatonic scales for melody, and backing chords live their own separate life.
In any case, if you want to do a Bm feel, you'll use a D note in the melody. Or if you use a D# note in the melody, you won't harmonize it with a Bm chord. Use both if you like.
Here's one in Em, with both Bm and B, chords first, placing melody notes on critical spots, with a rhythm. I guess it could go melody first as well, but if you write this melody without chords, you won't need a musical genius to come up with these chords.
Edit: I'll add my comment about the "going up" vs "going down" thing here. What happens with the melodic minor scale when going up is, it implies chords, namely secondary dominant - dominant - tonic. For example if the key has been established as Em, then even if played without accompaniment, the melody notes B - C# - D# - E feel like chords B - F#7 - B7 - Em. For some reason the melodic minor scale is often explained as some kind of natural phenomenon or semi-physical thing in itself that "just works" when going up, but IMO it's like a common short melodic phrase, with chords virtually embedded in it. It outlines a chord progression.
Why the melodic minor is not used all that often in descending melody phrases is that it requires a bit more imagination to feel a sensible harmony progression there. For example Em - B7 - F#7 - Em makes much less sense than Em - F#7 - B7 - Em. What comes to the harmonic minor scale's B - C - D# - E, it sounds like e.g. the chords Em - Am - B7 - Em. And descending E - D# - C - B works too: Em - B7 - Am - Em is easy to imagine there.