By choosing SJPP you also choose for a challenge on day 1. It takes 4 to 5 hours to climb the Puerto de Ibañeta. So be prepared (or start in Pamplona). In May it can be cold on the Meseta (800 m above sea level) and in the Spanish mountains (1,300 m). Cycling the Camino Path is also a challenge. Sometimes the Path is steep. There are stones, dust, mud, water and walkers who don't like bikers passing them closely. Alternative: asphalt. So plan your track, a mix of asphalt and the Path. Avoid cycling the asphalt of the N-120. There's a lot of traffic on this main road (large trucks) and that makes cycling not that comfortable as you might wish. The distance is about 900 km (SJPP-Santiago) so sixteen days will be sufficient. You won't have to hurry. So you can enjoy your Camino by visiting little villages (Estella, Nájera, Santo Domingo, Hontanas and many other), cities like Burgos and León, monastries and churches. And -very important- enjoy your Spanish food/meals. Tapas, cerveza, vino and the daily 'Pilgrims' meal' are my favorites. It'll be very helpful if you can understand (and speak) some elementairy Spanish. Older Spanish people only speak Spanish. And there're a lot of old Spaniards along the Camino. English is popular in contacts between pilgrims, coming from the UK, Netherlands, Germany, USA, Canada, Australia etc. Young people from France, Italy and Spain mostly speak English, sometimes even quite good. Enjoy these contacts.
Buen Camino!