But that's all that I've been able to discover. The relevant volume of the British Official History, Victory in the West, volume 2, The Defeat of Germany, doesn't mention it. I'd particularly like to know where the raid took place, since I'm trying to locate all the major British units in Belgium and the Netherlands in late 1944, but any information at all about it might give me keywords for further searches.
A few more hours work, and help from commenters has convinced me that if Operation Bogart existed, it was quite small and not terribly significant.
4th Commando Brigade (formerly 4th Special Service Brigade) consisted of No. 4 Commando (a British Army unit) and Nos. 41, 47 and 48 (Royal Marine) Commandos. No. 46 (Royal Marine) Commando had been part of the brigade, but was replaced by No. 4 Commando. A Commando, in this usage, was a battalion-sized unit. The whole brigade took part in Operation Infatuate, the seizure of the island of Walcheren, starting on 1st November 1944 and finishing on 8th November.
No. 4 was on Walcheren until 14th November, then near Zeebrugge, Belgium to re-equip and replace troops, then back to Walcheren for guarding it via raids on Schouwen-Duiveland.
No. 41 “served on the Maas river” after Infatuate for the rest of the war, seemingly based at Bergen-op-Zoom.
No. 47 was near Zeebrugge, from 10th November to 22nd December, when they became mobile reserve for British 1 Corps. They patrolled in anticipation of a German attack towards Antwerp, but the only action was against enemy fighting patrols. On 13-14 January they raided Kapelsches Veer, an island in the Maas, but withdrew after meeting heavy opposition.
No. 48 was also on the Maas, raiding, for the rest of the war, with a large part of it under No. 47 command.
There were clearly several raids, in addition to many patrols. Some of those raids may have had code names, but if so, they weren't significant enough to make it into theatre-level histories. My main source for all this is a compilation of Royal Marine unit histories, which makes it quite clear that there were no brigade-level operations after Operation Infatuate.
I suspect that the online hints of a brigade-level operation may have arisen out of confusion between 4th Commando Brigade, and No. 4 Commando, a sub-unit of the brigade. That suggests that Bogart may have been a smaller-scale operation by No. 4 Commando on Schouwen-Duiveland. However, knowing that there wasn't a brigade operation answers my immediate questions.