The standard pronuncation of 'bathed' in both British English and American English is /beɪðd/.
In Southern British English, 'bath' (noun) is pronounced [bɑːθ] while the verb 'bathe' is pronounced [beɪð]. The voiced 'th' [ð] is a remnant of Old English. And in Old English, it was a result of Intervocalic Fricative Voicing.
It's not correct to omit the final d but you'll hear the pronunciation without d a lot.
Most speakers pronounce the d but it's unreleased.
The reason you don't hear the d is that it's usually unreleased (i.e. [beɪðd̚]) at the end. But when it's followed by a vowel, then the d can be released and you'll often hear it. (Context will tell you which form of verb is used.)
How to articulate [ðd]: You can articulate the [ð] in two ways: dentally and Interdentally.
For dental [ð], you put the tip of your tongue against the back of the top teeth.
For interdental [ð], you stick out the tongue between the top and bottom teeth.
It depends on how much the tongue sticks out between the teeth.
For [ðd] in 'bathed', you articulate the [ð] (either dentally or Interdentally) and then move the tip of your tongue to the alveolar ridge and build a pressure for articulating the [d] but the air is usually not released (i.e. no puff of air).
Note: Some people might release the d at the end of 'bathed' and you'll hear a clear d. It depends on how you pronounce it.
(Fricative Voicing handouts - PDF).