We present an analysis of an 8 arcminute diameter map of the area around the galaxy cluster Abell 1835 from jiggle map observations at a wavelength of 1.1 mm using the Bolometric Camera (Bolocam) mounted on the Caltech Submillimeter Observatory (CSO). The data is well described by a model including an extended Sunyaev-Zel'dovich (SZ) signal from the cluster gas plus emission from two bright background submm galaxies magnified by the gravitational lensing of the cluster. The best-fit values for the central Compton value for the cluster and the fluxes of the two main point sources in the field: SMM J140104+0252, and SMM J14009+0252 are found to be \(y_{0}=(4.34\pm0.52\pm0.69)\times10^{-4}\), 6.5\(\pm{2.0}\pm0.7\) mJy and 11.3\(\pm{1.9}\pm1.1\) mJy, where the first error represents the statistical measurement error and the second error represents the estimated systematic error in the result. This measurement assumes the presence of dust emission from the cluster's central cD galaxy of \(1.8\pm0.5\) mJy, based on higher frequency observations of Abell 1835. The cluster image represents one of the highest-significance SZ detections of a cluster in the positive region of the thermal SZ spectrum to date. The inferred central intensity is compared to other SZ measurements of Abell 1835 and this collection of results is used to obtain values for \(y_{0} = (3.60\pm0.24)\times10^{-4}\) and the cluster peculiar velocity \(v_{z} = -226\pm275\) km/s.