Pretrained transformer-based language models have produced state-of-the-art performance in most natural language understanding tasks. These models undergo two stages of training: pretraining on a huge corpus of data and fine-tuning on a specific downstream task. The pretraining phase is extremely compute-intensive and requires several high-performance computing devices like GPUs and several days or even months of training, but it is crucial for the model to capture global knowledge and also has a significant impact on the fine-tuning task. This is a major roadblock for researchers without access to sophisticated computing resources. To overcome this challenge, we propose two novel hybrid architectures called HybridBERT (HBERT), which combine self-attention and additive attention mechanisms together with sub-layer normalization. We introduce a computing budget to the pretraining phase, limiting the training time and usage to a single GPU. We show that HBERT attains twice the pretraining accuracy of a vanilla-BERT baseline. We also evaluate our proposed models on two downstream tasks, where we outperform BERT-base while accelerating inference. Moreover, we study the effect of weight initialization with a limited pretraining budget. The code and models are publicly available at: www.github.com/gokulsg/HBERT/.