The Black Death entered southwestern England in summer 1348 and by all accounts struck Bristol with shocking force. Rumours of a terrible plague sweeping like wildfire across Europe had been rumbling for some time, and it is not surprising that the vibrant trading port of Bristol was the first major town in Britain to be affected, for it had close connections with the continent. Bristol was the second largest city in Britain and was the principal port of entry for the West Country. Within it lived upwards of 10,000 souls, tightly packed together in conditions that were not altogether sanitary.

'Filth running in open ditches in the streets, fly-blown meat and stinking fish, contaminated and adulterated ale, polluted well water, unspeakable privies, epidemic disease, - were experienced indiscriminately by all social classes.' (Holt and Rosser, The English Medieval Town, (1990))

Hythe Ossuary: remains of Black Death victims 

The foul conditions was as true of Bristol as it was of any other medieval town, if not more so because of its size and importance. People had a tendency to empty their chamber pots out of their windows into the street. Many houses owned their own pigs, which were supposed to be grazed outside the city walls, but were often allowed to roam the streets in search of food. Most townsfolk drew their water from the river, which was also used for industrial purposes by the local brewers, who were heavily regulated to prevent their fouling the water.

'...At this period the grass grew several inches high in the High St and in Broad St; it raged at first chiefly in the centre of the city.' (Geoffrey the Baker, Chronicon Angliae)

'The seventh year after it began, it came to England and first began in the towns and ports joining on the seacoasts, in Dorsetshire, where, as in other counties, it made the country quite void of inhabitants so that there were almost none left alive. From there it passed into Devonshire and Somersetshire, even unto Bristol, and raged in such sort that the Gloucestershire men would not suffer the Bristol men to have access to them by any means. But at length it came to Gloucester, yea even to Oxford and to London, and finally it spread over all England and so wasted the people that scarce the tenth person of any sort was left alive.' (Geoffrey the Baker, Chronicon Angliae)

     Conclusion  

It is quite possible that the Bridewell police station was built on or near to some of these burial sites.

Which could explain some of the findings on the night the gbhw research team carried out an investigation in the old Bridewell police station building on a cold March night.

We split up into separate groups so as to cover as much of the building as possible.
The cells were found to be the most active.  As we experienced stone throwing, and the feeling of being touched.  One of the ladies felt as though her necklace was being lifted but was too frightened to say anything at the time and kept her hand over it, in case it was snatched from her.
Others reported seeing flickering lights in and around the cells area.  There was a feeling of nausea and odd smells drifting in and out while sitting in these areas.
One of our mediums felt sure that there was a person sitting in the corner of the main holding cell.  Just sitting as though watching our movements.  There were also light anomalies caught on night vision cameras, one in particular seemed to direct it’s self toward Claire.
All groups reported similar experiences whilst down in the cells area.

It was found that the top floor was as active as were the cells.
One group reported that one of their cameras switched it’s self on and off at will.  They tried an experiment, by placing the camera on the radiator, when asking the spirit or what ever was in the room with them to switch the camera off it did so promptly.  No explanation has been found as to why or how it happened.

Later another group experienced activity on this top floor.
The first room to be investigated was bare except for a hand basin.
While asking if there was any spirit in there with them to show them selves in any way they could.  The tap in the hand basin turned it self on.  
In the next room, which was fitted out as a kitchen, had cupboards, wall cabinets and a sink with drainer.
After some time had passed in there calling for any thing to show or touch us in any way, suddenly there was an item which seemed to have been thrown with some force onto the sink drainer.  On examination we found an air gun pellet in the sink. Our host did explain that there were pellets of this kind on site, but could not explain how this one came to be in this room or land onto the sink as it did.  
Another unsolved mystery.

An excellent first night, but will have to return for a more in-depth investigation.