Did it buy any? Did it lend any money to those who had? If so, your bank was a direct beneficiary TARP.
Yes, it did. Banks who were technically insolvent suddenly got strong, largely risk-free assets in the place of assets who's market value had dropped to nill. That's a bailout, by any definition.
Similarly, banks who didn't have any toxic assets, but instead had leant money to banks who did have such assets, now saw their creditors who would have defaulted on their payments surviving and paying on time. That in turn, stopped them getting into financial trouble. That's also a bailout.
Similarly, banks who had neither bought any toxic assets, nor leant money to those who did, continued to benefit from a banking industry and lending and cash network that had not collapsed, precisely because the government had acted as a guarantor for the industry, willing to pledge money to shore it up. That is in effect a bailout.
The banks in bad condition were allowed to fail. TARP was an equity injection into mostly strong banks that was designed to instill confidence in a scary market and prevent a run on deposits.
More specifically, it stopped those who had leant money to bankrupt banks going bankrupt themselves. Such banks were not 'mostly strong', they were staring down the barrel of a market collapse in which they would lose, potentially, far more money than they had as assets. The government stepped in to stop them going bankrupt.