A lack of advanced equipment and surging flood waters are hampering the relief efforts, which are taking place near the village of Mugling, 80 kilometres (50 miles) west of Kathmandu.
The driver's body has been recovered from the river bank, but the bus and its passengers appear to have disappeared without a trace.
In the east of the country, meanwhile, more are frantically digging for survivors after a massive landslide swept away a remote hill village.
Wednesday's disaster was initially thought to have buried alive almost 100 people at Bamti village in Ramechhap district, but on Friday officials said 41 people were either dead or unaccounted for.
They have so far recovered nine bodies.
Officials say the rescuers, who include soldiers and police, chased away a group of Maoist rebels trying to obstruct their efforts.
No one was injured in the minor clashes that followed.
Heavy rains
Nepal has suffered extensive flooding and landslides since particularly heavy monsoon rains began battering the kingdom, north-eastern India and Bangladesh over a month ago.
Rains have eased in recent days, although floods and landslides continue to affect both urban and rural areas.
The bus was knocked by a falling rock into the raging Trishuli river as it was travelling from the capital to the western hill town of Baglung along a mountain road.
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