Unfortunately, you cannot set a target or max bit rate for H.264 in a Quicktime Container in AE's Render Queue. Well, you can set a "limit," but it get a bit confusing. Your best bet is to send the composition to Media Encoder by the Add to Media Encoder Render Queue command under the Composition menu. Then choose H.264 from the Format list. It'll give you an H.264 codec in an MP4 wrapper ( more compatible than MOV files anyway) and the ability to set your Target/Max Bitrate.
Also, a 10 minute timeline from AE is kinda nuts! What sort of video are you building? It couldnt be broken down or have parts of it done in Premiere? I mean, sometimes, it's necessary to have a comp that long, just curious what your project is!