The primary difficulty with using transits to discover extrasolar planets is the low probability a planet has of transiting its parent star. One way of overcoming this difficulty is to search for transits in dense stellar fields, such as the Galactic bulge. Here I estimate the number of planets that might be detected from a monitoring campaign toward the bulge. A campaign lasting 10 nights on a 10 meter telescope (assuming 8 hours of observations per night and a 5'x5' field of view) would detect about 100 planets with radius $\rp=1.5 \rjup$, or about 30 planets with $\rp=1.0 \rjup$, if the frequency and distribution of planets in the bulge is similar to that in the solar neighborhood. Most of these planets will be discovered around stars just below the turn-off, i.e. slightly evolved G-dwarfs. Campaigns involving 1- or 4-m class telescopes are unlikely to discover any planets, unless there exists a substantial population of companions with $\rp > 1.5 \rjup$.

4 pages, 4 figures. Submitted to ApJ Letters