The first was pushed through a vent into the men's toilets at The Three Arches pub, while the second was thrown into the pub's beer garden.
The third was pushed through the front door of the Heath Community Centre.
No-one was injured but the police say the bleach could have caused irritation if it had been breathed in.
It could also have caused harm if it had come into contact with the skin, police said.
The containers thrown into the pub toilet and beer garden happened at around the same time at 1830 BST.
The later incident at the community centre happened at around 2050 BST.
Officers from South Wales Police want to speak to anyone who saw a silver convertible car, possibly a K registration, which was seen leaving the area of The Three Arches pub at the time of the incident.
Detective Inspector Cronick, from Rumney Police Station said: "No injuries were sustained as a result of this incident but it has caused concern among local residents, and we are treating it very seriously.
"We have increased patrols in the area to reassure people."
Anyone with information should contact Cardiff CID on 029 2022 2111 or call Crimestoppers anonymously on 0800 555 111.
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~03~RS~)