The correct IPA transcription of bed is /bɛd/. I don't know why they provide that transcription. As far as I know, there's no isolated 'e' in an IPA transcription (RP), unless we talk about a diphthong or a triphthong (not isolated any more).
Edit: Here's a note from Wikipedia:
While most dictionary publishers use /e/, the actual realisation is [ɛ~e̞].
Received Pronunciation - Wikipedia, the free encyclopedia