If I have a wireless repeater bridge, does this simply extend the range of the WiFi signal or can I also wirelessly connect to the wireless repeater i.e. modem -> wireless router -> wireless bridge -> wireless repeater -> wireless clients e.g. wireless laptop
A wireless repeated by definition extends the range of a wireless connection. It uses wifi to both connect to another AP and also to provide AP services to whatever is in range.
As there is usually only one radio involved, then this effectively halves the throughput of the wireless device. Any client originated packets first travel over the air to the repeated bridge, which then forwards them over the air to the headend AP. So there are double the amount of packets in the air as compared to a simple client->AP setup.
Note that your diagram is a little off, it would look more like: