Dear Jane Doe,

I got your name from [where you found them] and thoroughly enjoyed your review of [name of book]. I recently wrote a book that appeals to a similar audience, “[Name of my book].” If you think you might be interested in reading it and perhaps reviewing it, I’ll gladly send you complimentary copy.

Thank you so much for your time,

Best Regards,

[Author Name]

[Your website]

[Your social media links]