Definitely check the waarneming.nl website before going out, because likely there will be some rarities and temporary concentrations of birds during your visit. This part of the Netherlands is very birded, and you will have up to date information. See on waarnemingen that only some spots and ponds among many are good for birds, and these are invariably well known. When in the field, look for groups of excited birders as much as for the birds.
I think the best day car trip from Amsterdam is actually the peninsula before Texel: Campenduin, Balgzandpolder, Balgzand, Den Oever, Wieringenwerf and if time allows, some coast spots around Hyppolytushoef. The habitats and concentrations of birds are the same as Texel, but you don't waste time on the ferry. Texel is a bit awkward because it is slightly too big for a bicycle (25km) but costly to take a car. This may, of course, change if there is a major rarity elsewhere.
That route will probably get you the biggest diversity of species, but some individual ones will not be there: Purple Heron is mostly S of Amsterdam etc. Definitely check also the tide chart, because there will be good concentrations of birds at the high tide, even if April is not the peak shorebird migration. Take care of traffic jams in peak times.