We describe a time-resolved nascent single-cell RNA sequencing (RNA-seq) approach that measures gene-specific transcriptional noise and the fraction of active genes in S.cerevisiae. Most genes are expressed with near-constitutive behavior, while a subset of genes show high mRNA variance suggestive of transcription bursting. Transcriptional noise is highest in the cofactor/coactivator-redundant (CR) gene class (dependent on both SAGA and TFIID) and strongest in TATA-containing CR genes. Using this approach, we also find that histone gene transcription switches from a low-level, low-noise constitutive mode during M and M/G1 to an activated state in S phase that shows both an increase in the fraction of active promoters and a switch to a noisy and bursty transcription mode. Rapid depletion of cofactors SAGA and MED Tail indicates that both factors play an important role in stimulating the fraction of active promoters at CR genes, with a more modest role in transcriptional noise.