Some beachgoers made hand gestures and disapproving noises while a man told Alshelh he would call the police if she refused to leave.
"There shouldn't be a connection between terrorism and the burkini and there shouldn't be a connection between terrorism and Islam altogether," she said.
Dozens of French resorts banned the full-body swimwear following the massacre of 86 people on Nice seafront in July. Isis (Islamic State) terror group claimed responsibility for the attack.
Manuel Valls, the French Prime Minister, described the swimsuit worn by some Muslim women as a symbol of the "enslavement of women" - but human rights campaigners said burkini bans unfairly targeted Muslims.
Their view was backed by the Council of State, the administrative court. It ruled last month that the bans breached civil liberties and found that officials had failed to prove that the swimsuit posed a threat to public order.
However, many French resorts have continued to enforce their bans, under which women can be fined for wearing the burkini. Earlier this month a lower court in Corsica upheld a local ban decreed by a mayor.
The burkini originated in Australia, where it was introduced in 2004 by an Australian-Lebanese designer, Aheda Zanetti. Zanetti said it was not a religious garment and she designed it to allow more Muslim women to take part in swimming and other sports. Her intention, she said, was "to give women freedom, not to take it away".
Alshelh said she visited France to speak to local Muslim women "who have gone through this kind of stuff," adding that the burkini had allowed her to combine her religion with her love of sports, including karate, which she has practised since the age of 11.