As most of the books are focused on Harry, it is only the conversations that he is present for that are recorded. The first 3 books are more for younger children, so there's not a lot of discussion (if any) about men/boys in any case - and hardly any interaction between female characters at all.
Book 1: The Philosopher's Stone. No. The focus of the book is on Harry. The main female interactions are his Aunt, various Professors and Hermione - but primarily with Harry.
Book 2: The Chamber of Secrets. Yes. I guess. Hermione talks to Moaning Myrtle (the ghost) - but only for a sentence or two.
Book 3: The Prisoner of Azkaban. No.
From book 4 onward, the focus of the story shifts about a little, though it's still primarily limited to Harry's POV.
Book 4: The Goblet of Fire. Yes. (page 230) Again. not much of a conversation, Hermione wishes Angelina well for entering the contest. (page 330) Hermione talks to Winky, a freed female house-elf, about employment. Only a couple of sentences. (page 391/2) Hermione has a terse interchange with Rita Skeeter.
Book 5: Order of the Phoenix. Yes. (Page 78) Mrs Weasley and Tonks interact about assistance in the kitchen. All of 2 sentences each. (Page 81) Not so much a conversation here, but Tonks entertains Hermione and Ginny by transforming her nose. (Page 86/87) Mrs Weasley tells Ginny to go to bed and there are a couple of sentences describing Ginny's reaction. (Pages 131-133) Madam Bones questions Mrs Figg during Harry's trial. (Page 155) Ginny and Tonks discuss in a couple of sentences why Tonks was never a prefect. (Page 165) Tonks tells Mrs Weasley to hurry up. (Page 168) Ginny and Luna interact in a Hogwarts Express compartment. (Page 175) Hermione rubbishes the Quibbler and Luna gets annoyed. (Pages 217-221) Hermione interacts with Dolores Umbridge; as does Parvati Patil. It doesn't go well. (Page 234) Hermione answers Professor Grubbly-Plank's questions about Bowtruckles. (Page 280-282) Umbridge checks on Professor Trelawney. (Page 283/284) Hermione crosses Umbridge. (Page 286/287) Umbridge checks on Professor McGonagall. (Page 288/289) Umbridge checks on Professor Grubbly-Plank. (Page 308) Hermione argues with Luna and Ginny breaks it up. (Page 325/6) Parvati has a conversation with Professor Trelawney that lasts for about a page. (Page 367/8) Professor McGonagal and Umbridge have another encounter. (Page 396) Umbridge asks Pansy Parkinson a question and gets an answer. (Page 498-502) Hermione and Luna talk to Rita Skeeter. (Page 524/5) Umbridge tries to evict Professor Trelawney. (Page 528) Hermione talks to Lavender. (Page 584-587) Professor McGonagal and Umbridge clash during Harry's careers discussion. (Page 626/7) Umbridge talks to Professor Marchbanks. (Page 638) Angelina Johnson, Hermione, Katie Bell, Lavender and Alicia Spinnet take part in a conversation about Hagrid's sacking. (Page 649) Luna and Ginny talk with Hermione while planning how to get to the Department of Mysteries. (Page 658-660) Hermione stops Umbridge from torturing Harry. (Page 662-664) Hermione leads Umbridge into the Forbidden Forest. (Page 681) Ginny, Luna and Hermione help identify a tank of brains. (Page 747/8) Hermione talks to Luna and Ginny. Umbridge (vaguely) talks to Madame Pomfrey.
Book 6: Half-Blood Prince. Yes. (Page 26/27) Bellatrix and Narcissa talk before meeting Snape. (Page 91) Fleur Delacour brings Harry his breakfast tray while talking to Mrs Weasley. (Page 118) Ginny asks her mother for a Pygmy Puff. (Page 233) The argument that Katie Bell has with her friend, Leanne, is identified only by Harry being aware of their voices and by a single sentence from Katie herself. So I don't think that counts as a conversation. (Page 235/6) Hermione talks to Leanne. (Page 293) Hermione talks to Parvati about going to Slughorn's party. (Page 297) Hermione and Luna talk to Professor Trelawney at the party.
Book 7: The Deathly Hallows. Yes. (Page 203) Umbridge talks to Hermione (polyjuiced as Mafalda Hopkirk) in the Ministry elevator. (Page 213/4) Umbridge interrogates Mary Catermole. (Page 215) Hermione as Mafalda talks to Umbridge. (Page 378) Bellatrix tortures Hermione. (Page 413) Luna talks to Hermione. (Page 483) Professor McGonagall and Professor Sprout discuss tactics for protecting Hogwarts and the students. (Page 486) Mrs Weasley tries to stop Ginny from taking part in the defense of Hogwarts. (Page 489) Professor McGonagall answers some questions from Slytherin girls. (Page 532/3) Lily and Petunia talk about Lily's magic. (Page 536-538) Lily talks to Petunia about Hogwarts and Petunia calls her a 'freak'. (Page 590) Mrs Weasley fights Bellatrix.
Based on what I've seen, I have to say that of the first 4 Harry Potter books, 2 don't appear to meet the criteria for passing the Bechdel test, while the other 2 barely pass. Though there are multiple women characters (the most major being Hermione) in it, they don't tend to interact with each other.
This changes with Book 5 - though the interactions still tend to be short, there are certainly more women characters talking to each other and (so far) definitely not about men.
Book 6 has fewer interactions between female characters than Book 5, but it also has some interactions where the women are discussing romantic entanglements.
Book 7 is back to fewer interactions between female characters, though this is unsurprising as it is mostly Harry. Ron and Hermione trying to find Horcruxes and a way to destroy them.
Overall, the series appears to meet the simplest version of the Bechdel test - though if there was a requirement for no men to be present during the conversation, it is likely that only Book 6 would pass due to Bellatrix and Narcissa talking prior to meeting Snape; every other conversation has Harry present. If there was a requirement for a minimum length of interaction, most of these examples would have to be removed as they tend to be limited to one or two sentences spoken by the women to each other - more of a passing comment than a conversation.