Accurate estimation of bite rate, i.e., the number of bites during a given grazing period, is important for the characterisation of cattle grazing behaviour and feed intake. In this paper, we estimate the bite rate of grazing cattle from accelerometer data using semi-supervised linear regression. We use a mixture of labelled and unlabelled accelerometer data collected during the grazing trial to train the semi-supervised model. The labelled data has associated ground-truth values for the bite rate and was recorded by an expert observer at intermittent times over the duration of the trial. The trial involved ten cattle, each fitted with a tri-axial accelerometer mounted on a neck collar, over a period of five weeks. We calculate various features from tri-axial accelerometer data and utilise several feature selection approaches and regression methods to fit bite-rate prediction models to our data and compare their performance. Our leave-one-animal-out cross-validated results show that a semi-supervised linear regression model with the specifically chosen feature set delivers good bite-rate prediction performance with a root mean squared error of 5.73 bites per minute and an R2 value of 0.73. Other regression models tested here (including orthogonal distance regression) yielded similar results.