Phosphorus-enhanced (P-rich; [P/Fe] ≳ +0.8) giants have been found among mildly metal-poor field stars, but in only one star in a globular cluster (GC), M4 (NGC 6121). Also, in a sample of bulge spheroid stars, some of them showed a moderate P enhancement in the range +0.5 < [P/Fe] < +1.0. In this paper we derive the P abundance of moderately metal-poor ([Fe/H] ≳ ‑1) GC stars, aiming to check if the phenomenon could be related to the unusual multiple stellar populations found in most GCs. Here we present the detection of moderately P-enhanced stars among two out of seven bulge GCs (Tonantzintla 1 and NGC 6316), with metallicities similar to those of the bulge-field P-rich stars. Using H-band high-resolution (R ∼ 22,500) spectra from the APOGEE-2 survey, we present the first high-resolution abundance analysis of [P/Fe] from the P I 16482.932 Å line in a sample of selected bulge GCs. We find that all P-rich stars tend to also be N-rich, which hints at the origin of P-rich stars as second-generation stars in GCs. However no other correlations of P and other elements are found, which are usually indicators of second-generation stars. Further studies with larger samples and comparisons with field stars will be needed before any firm conclusions are drawn.