The B4A Bridge is just an App which allows you to connect to the phone using the B4A IDE and Debug your code. It works using WiFi and there is no requirement to installed to an SD card.
Also, with regard to Manfred's last post. Only licenced users can download libraries. It's one of the restrictions of the trial licence in afraid. But I'm certain that you won't regret purchasing B4A, as many can attest to here. The support is absolutely first class!