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Increasing cycling for transportation or recreation can boost health and reduce the environmental impacts of vehicles. However, news agencies' ideologies and reporting styles often influence public perception of cycling. For example, if news agencies overly report cycling accidents, it may make people perceive cyclists as "dangerous," reducing the number of cyclists who opt to cycle. Additionally, a decline in cycling can result in less government funding for safe infrastructure. In this paper, we develop a method for detecting the perceived perception of cyclists within news headlines. We introduce a new dataset called ``Bike Frames'' to accomplish this. The dataset consists of 31,480 news headlines and 1,500 annotations. Our focus is on analyzing 11,385 headlines from the United States. We also introduce the BikeFrame Chain-of-Code framework to predict cyclist perception, identify accident-related headlines, and determine fault. This framework uses pseudocode for precise logic and integrates news agency bias analysis for improved predictions over traditional chain-of-thought reasoning in large language models. Our method substantially outperforms other methods, and most importantly, we find that incorporating news bias information substantially impacts performance, improving the average F1 from .739 to .815. Finally, we perform a comprehensive case study on US-based news headlines, finding reporting differences between news agencies and cycling-specific websites as well as differences in reporting depending on the gender of cyclists. WARNING: This paper contains descriptions of accidents and death.