No. TunnelBear follows a strict no-logging policy. It does not store records of the sites you browse, your DNS queries, when you connect, or your IP addresses. While you are connected, nothing about your online activity is recorded, watched or saved in a form that could point back to you or reveal what you did on the web.
There is just one piece of information TunnelBear keeps: a single combined number showing how much bandwidth each account consumed in a billing period. It exists only so the free plan's monthly data cap (500 MB) can be applied and paid plans can be billed. It says nothing about which websites you opened or what you sent — it is merely a byte total, much like your mobile carrier tallying the megabytes you used this month.
These no-logging promises are more than marketing copy. Every year Cure53, an independent cybersecurity company, checks them, and its audit looks closely at whether the infrastructure is even capable of producing activity logs. Its conclusions repeatedly confirm that TunnelBear's architecture is built so that detailed logs cannot be gathered. All the published audit reports are available to read on TunnelBear's website.