When Rivka first saw Yitzchak, the pasuk says “She fell off the camel” (Bereishis 24:64). This means as soon as she spotted him she immediately slipped off the camel. The R’dak explain (in his commentary to the Torah) that on hearing he was Yitzchok she “dived for cover”. Due to her modesty and bashfulness, she hid herself from her choson rather than appear immediately before him face to face.
A further reason for slippling immediately off the camel is given by the Rambam. She had been riding the camels back with her legs apart in order to maintain a proper grip and ensure her safety. Now that she saw Yitzchok coming to her, she felt it would be distictly unrefined to remain in that position. She therefore slipped off the camel as quickly as possible.