Given large language models' (LLMs) increasing integration into workplace software, it is important to examine how biases in the models may impact workers. For example, stylistic biases in the language suggested by LLMs may cause feelings of alienation and result in increased labor for individuals or groups whose style does not match. We examine how such writer-style bias impacts inclusion, control, and ownership over the work when co-writing with LLMs. In an online experiment, participants wrote hypothetical job promotion requests using either hesitant or self-assured autocomplete suggestions from an LLM and reported their subsequent perceptions. We found that the style of the AI model did not impact perceived inclusion. However, individuals with higher perceived inclusion did perceive greater agency and ownership, an effect more strongly impacting participants of minoritized genders. Feelings of inclusion mitigated a loss of control and agency when accepting more AI suggestions.