The paradigmatic example of deconfined quantum criticality is the Neel to valence bond solid phase transition. The continuum description of this transition is the N=2 case of the CP^{N-1} model, which is a field theory of N complex scalars in 3D coupled to an Abelian gauge field with SU(N)×U(1) global symmetry. Lattice studies and duality arguments suggest the global symmetry of the CP^{1} model is enhanced to SO(5). We perform a conformal bootstrap study of SO(5) invariant fixed points with one relevant SO(5) singlet operator, which would correspond to two relevant SU(2)×U(1) singlets, i.e., a tricritical point. We find that the bootstrap bounds are saturated by four different predictions from the large N computation of monopole operator scaling dimensions, which were recently shown to be very accurate even for small N. This suggests that the Neel to valence bond solid phase transition is described by this bootstrap bound, which predicts that the second relevant singlet has dimension ≈2.36.