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I recently got a Görlitz-Meyer Optik Telemegor 250mm F5.5

I am using this telephoto-lens on my Sony a6300 APS-C camera and I like it.
The problem I currently have is, that I get a lot of "bloom" in my pictures.

This lets my subjects appear glowing, like this dove flying away.

While being quite a neat effect, I would like to know, if this is a optical limitation or if it can be caused by dust inside the lens ? (like bacteria growing to fungus)

It appears this is somewhat typical of the MOG 250 mm lens. Based on examples at Flickr and elsewhere, the lens exhibits characteristic ring-shaped or bubble background bokeh, and dreamy haze at the plane of focus (especially when shooting wide open aperture). It's possible your copy of the lens exaggerates the effect — all lenses of a particular make/model exhibit copy-to-copy variations — and it's possible the effect could be exacerbated by dust in the lens. But the presence of the effect itself is due to the design of the lens.

If dust is a factor, it appears the lens is fairly easy to disassemble and clean, if you're inclined to tackle that yourself.

This reminds me of the adjustable effect on Nikon's DC 105mm ƒ/2 and DC 135mm ƒ/2 lenses (DC = "defocus control"). Those lenses allow a degree of control over the quality of the bokeh (with an inverse relationship on the foreground bokeh). The effects of the MOG 250mm appear similar to one of the Nikon DC lenses set to rear defocus, which causes positive spherical aberration. From jrista's answer to the question, How do soft focus or defocus control rings work?,

(Reference: David Pinkerton @ Flickr)

The above image was taken with the Nikkor 135mm f/2 lens with defocus control, set to REAR f/4. Note the dreamy effect of highlights right around the plane of focus, and the ringed background bokeh. Both are effects of positive spherical aberration caused by the brighter edges and darker centers of OOF blur circles. Foreground blur will be smooth and creamy without the dreamy effect. For portraits, the same effect can be used to give that dreamy glow to hair, earrings or glasses, anything that produces a bright specular highlight.

Meyer-Optik Görlitz lenses are known for their bubble bokeh. Usually a "glow" or halo, what you describe as "bloom", is also seen in such lenses. Both appear to be associated with spherical aberration. To control them, stop down. Sometimes, only a fraction of a stop is needed.

It is possible for dust, fungus, and haze to cause similar effects. See soft-focus.